understAnding icse MAtheMAticsjesusandmary.in/notices/ICSE Maths 10 Sec-1 Chps 1-3.pdf · 2020. 4. 23. · ICSE examinations. The subject matter contained in this book has been explained

[Strictly according to the latest Syllabus prescribed by the Council for the Indian School Certificate Examinations, New Delhi for

Class X Examinations for the year 2021 and onwards]

by

M.L. AggArwALFormer Head of P.G. Department of Mathematics

D.A.V. College, Jalandhar

AvichAL PubLishing coMPAnyIndustrial Area, Trilokpur Road, Kala Amb 173 030, Distt. Sirmour (HP)

Delhi Office : 1002 Faiz Road (opp. Hanumanji Murti), Karol Bagh, New Delhi-110 005

Class X

understAndingicse

MAtheMAtics

Published by :

Avichal Publishing companyIndustrial Area, Trilokpur Road,Kala Amb 173 030, Distt. Sirmour (HP)

Delhi Office:1002 Faiz Road (opp. Hanumanji Murti)Karol Bagh, New Delhi - 110 005 (India)Phone: 011-28752604, 28752745, 28755383Fax: 011-28756921Website: www.apcbooks.co.inEmail: [email protected]

© Author

ISBN-978-81-7739-564-8

First Edition: 1994Twenty Second Edition: 2019twenty third edition: 2020 (thoroughly revised)

Price: ` 480.00

Laser Typeset at:Laser tech Prints

Printed at:Parmanand offsetDelhi

The book has been published in good faith that the material provided by the author is original.All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means [graphic, electronic or mechanical, including photocopying, recording, taping or information retrieval system] without the written permission of the copyright holder, application for which should be addressed to the publisher. Such written permission must also be obtained before any part of this publication is stored in a retrieval system of any nature. Breach of this condition is liable for legal action.Exhaustive efforts have been made to ensure accuracy and correctness of contents of the book at the time of going to press. However, in view of possibility of human error, neither the author, publisher nor any other person who has been involved in preparation of this work accepts any responsibility for any errors or omissions or results obtained from use of information given in the book.The publisher shall not be liable for any direct, consequential, or incidental damages arising out of the use of the book.In case of binding mistake, misprints, or missing pages etc., the publisher’s entire liability, and your exclusive remedy, is replacement of the book within one month of purchase by similar edition/reprint of the book. Any mistake, error or discrepancy noted may be brought to our notice which shall be taken care of in the next edition. In case of any dispute, all legal matters are to be settled under Delhi Jurisdiction only.

beware of duPLicAte books

We do not have any policy of selling soiled/badly printed books as rejected lots in the market. Kindly beware of duPLicAte books sold as so called rejected lots.

Publication ofKey to this bookis strictly prohibited.

This book was first published in 1994. Twenty-two editions and a number of reprints published during these years show its growing popularity among students and teachers. The book has been revised thoroughly again strictly conforming to the latest syllabus issued by the Council for ICSE examinations.

The subject matter contained in this book has been explained in a simple language and includes many examples from real life situations. Emphasis has been laid on basic facts, terms, principles, concepts and on their applications. Carefully selected examples consist of detailed step-by-step solutions so that students get prepared to tackle all the problems given in the exercises.

A new feature ‘Multiple Choice Questions’ has been added in each chapter. These questions have been framed in a manner such that they holistically cover all the concepts included in the chapter and also, prepare students for the competitive exams. This is further followed by a ‘chapter test’ which serves as the brief revision of the entire chapter.

An attempt has been made to make the book user friendly — matter is well spaced out and divided into sections and sub-sections which have been differentiated by using headings of different sizes and colour, thus reducing the strain on the eyes of the students and giving the book a neat and uncluttered look. It has been my sincere endeavour to present the concepts, examples and questions in a coherent and interesting manner so that the students develop interest in ‘learning’ and ‘understanding’ mathematics.

I am grateful to my publishers ‘M/s Avichal Publishing Company’ and ‘Laser Tech Prints’ and thank them for their friendly cooperation and untiring efforts in bringing out this book in an excellent form. I would highly appreciate if you suggest any improvement you would like to see in the book in its next edition.

— M.L. Aggarwal

www.ilovemaths.com

Log in for Vedic mathematics, Indian mathematicians, Question-answering service and discussion forum moderated by Professor Theta, Classroom material, Model test papers and much more …

☞

Preface

(iv)

✰ This book is written strictly according to the latest syllabus prescribed by the council for ICSE examinations for the year 2021 and onwards.

✰ The subject material has been treated systematically and presented in a coherent and interesting manner.

✰ The theory has been explained in simple language and includes many examples from real life situations. Emphasis has been laid on basic facts, concepts, terms, principles and on the applications of various concepts.

✰ Carefully selected examples consist of detailed step-by-step solution. A number of solved examples are included in each section so that students are well prepared to tackle all the problems given in exercises.

✰ Each chapter is followed by a Chapter Test which includes problems related to all the topics, so that students have total understanding of these topics before going on to next chapter.

✰ An attempt has been made to make the book user friendly—matter is well spaced out and given in a bigger type size. Also, the matter has been broken into sections and subsections so that students can learn at their own pace.

✰ Each chapter contains an exercise on Multiple Choice Questions which have been framed in a manner such that they holistically cover all the concepts included in the chapter.

✰ The exercises are liberally sprinkled with questions from ICSE examination papers so that the students get familiarity with the types of questions to be found in the examination.

✰ This book is sufficient to help the students score cent-percent marks in ICSE examination and also builds a strong foundation for success in any competitive examination.

salient Features of This Book

chAPters PAge no.

Syllabus (vii)

Commercial Mathematics

1. Goods and Services Tax (GST) 1 2. Banking 20 3. Shares and Dividends 28

Algebra

4. Linear Inequations 44 5. Quadratic Equations in One Variable 56 6. Factorisation 96 7. Ratio and Proportion 110 8. Matrices 130 9. Arithmetic and Geometric Progressions 163

Coordinate Geometry

10. Reflection 196 11. Section Formula 211 12. Equation of a Straight Line 227

Geometry

13. Similarity 250 14. Locus 296 15. Circles 308 16. Constructions 377

Mensuration

17. Mensuration 389

Trigonometry

18. Trigonometric Identities 440 19. Trigonometrical Tables 462 20. Heights and Distances 465

Statistics

21. Measures of Central Tendency 482

Probability

22. Probability 523

Answers 547

Tables 571

Contents

(vi)

1. To acquire knowledge and understanding of the terms, symbols, concepts, principles, processes, proof, etc. of mathematics.

2. To develop an understanding of mathematical concepts and their applications to further studies in mathematics and science.

3. To develop skills to apply mathematical knowledge to solve real life problems.

4. To develop the necessary skills to work with modern technological devices such as calculators and computers in real life situations.

5. To develop drawing skills, skills of reading tables, charts and graphs.

6. To develop an interest in Mathematics.

There will be one paper of two and a half hours duration carrying 80 marks and Internal Assessment of 20 marks.

The paper will be divided into two sections. Section I (40 marks), Section II (40 marks).

section i: Will consist of compulsory short answer questions.

section ii : Candidates will be required to answer four out of seven questions.

Class – X

Mathematics Instructional Objective

structure of the Question Paper

(vii)

cLAss XThere will be one paper of two and a half hours duration carrying 80 marks and Internal Assessment of 20 marks.

The paper will be divided into two sections, Section I (40 marks), Section II (40 marks).

Section I : Will consist of compulsory short answer questions.

Section II : Candidates will be required to answer four out of seven questions.

1. coMMerciAL MAtheMAtics

(i) Goods and Services Tax (GST)

Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases. Candidates are also expected to find price paid by the consumer after paying State Goods and Service Tax (SGST) and Central Goods and Service Tax (CGST) – the different rates as in vogue on different types of items will be provided. Problems based on corresponding inverse cases are also included.

(ii) Banking

Recurring Deposit Accounts: computation of interest and maturity value using the formula:

I = P n n r( )+×

×1

2 12 100

MV = P × n + I

(iii) Shares and Dividends

(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium

(b) Fomulae

• Income=number of shares× rate of dividend×FV.

• Return= (Income / Investment)×100.

Note: Brokerage and fractional shares not included

2. ALgebrA

(i) Linear Inequations

Linear Inequations in one unknown for x ∈ N, W, Z, R.

•Solving algebraically andwriting the solution in setnotation form.

•Representation of solution on thenumber line.

(ii) Quadratic Equations in one variable

(a) Nature of roots

•Twodistinct real roots if b2 – 4ac > 0

•Two equal real roots if b2 – 4ac=0

•No real roots if b2 – 4ac < 0

(b) Solving Quadratic equations by:

•Factorisation

•UsingFormula

(c) Solving simple quadratic equation problems.

latest syllabus in Mathematics

(viii)

(iii) Ratio and Proportion

(a) Proportion, Continued proportion, mean proportion

(b) Componendo, dividendo, alternendo, invertendo properties and their combinations.

(c) Direct simple applications on proportions only.

(iv) Factorisation of polynomials:

(a) Factor Theorem

(b) Remainder Theorem.

(c) Factorising a polynomial completely after obtaining one factor by factor theorem.

Note: f (x) not to exceed degree 3.

(v) Matrices

(a) Order of a matrix, Row and column matrices.

(b) Compatibility for addition and multiplication.

(c) Null and Identity matrices.

(d)Addition and subtraction of 2×2matrices.

(e)Multiplication of a 2×2matrix by

• anon-zero rationalnumber

• amatrix

(vi) Arithmetic and Geometric Progressions

•Finding theirGeneral term

•Finding sumof theirfirst ‘n’ terms

•SimpleApplications.

(vii) Coordinate Geometry

(a) Reflection

(i) Reflection of a point in a line:

x=0, y=0, x= a, y= a, the origin.

(ii) Reflection of a point in the origin.

(iii) Invariant points.

(b) Coordinates expressed as (x, y), Section formula, Mid-point formula, Concept of slope, equation of a line, Various forms of straight lines.

(i) Section and Mid-point formula (Internal section only, coordinates of the centroid of a triangle included).

(ii) Equation of a line:

•Slope-intercept formy=mx+ c

•One-point form (y–y1)=m (x–x1)

Geometricunderstandingof‘m’asslope/gradient/tanθ where θ is the angle the line makes with the positive direction of the x axis.

Geometric understanding of ‘c’ as the y-intercept / the ordinate of the pointwhere the line intercepts the y-axis/the point on the linewhere x=0.

•Conditions for two lines to be parallel or perpendicular.

Simple applications of all the above.

(ix)

3. geoMetry

(a) Similarity

Similarity, conditions of similar triangles.

(i) As a size transformation

(ii) Comparison with congruency, keyword being proportionality.

(iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included).

(iv) Applications of Basic Proportionality Theorem.

(v) Areas of similar triangles are proportional to the squares of corresponding sides.

(vi) Direct applications based on the above including applications to maps and models.

(b) Loci

Loci: Definition, meaning, Theorems and constructions based on Loci.

(i) The locus of a point at a fixed distance from a fixed point is a circle with the fixed point as centre and fixed distance as radius.

(ii) The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines.

(iii) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

Proofs not required

(c) Circles

(i) Angle Properties

• The angled that an arc of a circle subtends at the centre is double thatwhich itsubtends at any point on the remaining part of the circle.

•Angles in the same segment of a circle are equal (without proof).

•Angle in a semicircle is a right angle.

(ii) Cyclic Properties:

•Opposite angles of a cyclic quadrilateral are supplementary.

• The exteriorangleof a cyclicquadrilateral is equal to theopposite interiorangle(without proof).

(iii) Tangent and Secant Properties:

• The tangent at any point of a circle and the radius through the point areperpendicular to each other.

• If two circles touch, the point of contact lies on the straight line joining theircentres.

• From any point outside a circle two tangents can be drawn and they are equalin length.

• If twochords intersect internallyorexternally thentheproductof the lengthsofthe segments are equal.

• If a chord and a tangent intersect externally, then theproduct of the lengths ofsegments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

• If a line touches a circle and from the point of contact, a chord is drawn, theangles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

note: Proofs of the theorems given above are to be taught unless specified otherwise.

(x)

(iv) Constructions

(a) Construction of tangents to a circle from an external point.

(b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.

4. MensurAtion

Area and volume of solids — Cylinder, Cone and Sphere.

Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

note: Problems on Frustum are not included.

5. trigonoMetry

(a)Using Identities to solve/prove simple algebraic trigonometric expressions

sin2A+ cos2A=1

1+ tan2A= sec2 A

1+ cot2A= cosec2 A; 0 ≤ A ≤ 90°

(b) Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

note: Cases involving more than two right angled triangles excluded.

6. stAtistics

Statistics — basic concepts, Mean, Median, Mode, Histograms and Ogive.

(a) Computation of:

• MeasuresofCentralTendency:Mean,median,mode for rawandarrayeddata.Mean*,median class and modal class for grouped data. (both continuous and discontinuous).

*Meanby all 3methods included:

Direct : ΣΣfxf

Short-cut : A+ΣΣfdfwhere d=x–A

Step-deviation : A+ΣΣ

ftf× iwhere t= x A

i−

(b) Graphical Representation. Histograms and Less than Ogive.

• Findingthemodefromthehistogram,theupperquartile,lowerquartileandmedianetc.from the ogive.

•Calculation of inter quartile range.

7. ProbAbiLity

•Random experiments

•Sample space

•Events

•Definition of probability

•Simple problems on single events

(xi)

Agreed Conventions (a) Units may be written in full or using the agreed symbols, but no other abbreviation

may be used. (b) The letter ‘s’ is never added to symbols to indicate the plural form. (c) A full stop is not written after symbols for units unless it occurs at the end of a

sentence. (d) When unit symbols are combined as a quotient, e.g. metre per second, it is

recommended that they may be written as m/s or better still as m s–1. (e) Three decimal signs are in common international use : the full point, the mid-point

and the comma. Since the full point is sometimes used for multiplication and comma for spacing digits in large numbers, it is recommended that the mid-point be used for decimals.

S.I. UnItS (International System of Units)

Basic S.I. Units

Quantity Unit ofMeasure Symbol

Length metre m

Mass/Weight kilogram kg

Capacity litre L

Time second s

Measures of Length

Symbols10 millimetres = 1 centimetre 10 mm = 1 cm100 centimetres = 1 metre 100 cm = 1 m1000 metres = 1 kilometre 1000 m = 1 km

Measures of Mass/weight

10 milligrams = 1 centigram 10 mg = 1 cg100 centigrams = 1 gram 100 cg = 1 g1000 grams = 1 kilogram 1000 g = 1 kg100 kilograms = 1 quintal10 quintals = 1 metric tonne

Measures of capacity

10 millilitres = 1 centilitre 10 mL = 1 cL100 centilitres = 1 litre 100 cL = 1 L1000 litres = 1 kilolitre 1000 L = 1 kL

s.I. units, symbols and abbreviations

square and cubic units

1 cm2 = 100 mm2 1 cm3 = 1000 mm3

1 m2 = 10000 cm2 1 m3 = 1000000 cm3

commonly used equivalents

1 litre = 1000 cm3

1 m3 = 1000 litres1 hectare (ha) = 10000 m2

Measures of time

60 seconds = 1 minute 60 s = 1 min60 minutes = 1 hour 60 min = 1 h24 hours = 1 day 24 h = 1 dy7 days = 1 week30 days = 1 month365 days = 1 year (366 days = 1 leap year)

SymbolS And AbbrevIAtIonSImplies that ⇒ logically equivalent to ⇔identically equal to ≡ approximately equal to »belongs to ∈ does not belong to ∉is equivalent to ↔ is not equivalent to ↔

union ∪ intersection ∩contains ⊃ is contained in ⊂universal set ξ the empty set ϕnatural numbers N whole numbers Wintegers I or Z real numbers Ris parallel to is perpendicular to ⊥is congruent to ≅

(xii)

Goods and Services Tax 1

introductionGoods and Services Tax (GST) is an indirect tax levied on the supply of goods and services i.e. on the sale of goods and rendering services. It is a nation-wide tax which subsumes several indirect taxes levied by the Centre and State Governments and is based on the principle of 'One nation one tax'.

Central level taxes merged into GST are – Excise Duty, Custom Duty, Service Tax and Central Sales Tax. State level taxes merged into GST are – Octroi and Entry Tax, Value Added Tax (VAT), Entertainment Tax, Taxes on Lottery and Luxury Tax etc.

GST creates a semblance of common market where every supply of goods or services or both irrespective of where it takes place has common treatment and a defined common tax rate throughout the chain.

1.1 goods and services taxGoods and Services Tax (abbreviated GST) is an indirect tax levied on the supply of goods and services.

1.1.1 some terms related to gst1. Dealer. Any person who buys goods or services for resale is known as a dealer (or trader). A

dealer can be a firm or a company. Only a dealer (person or firm or company) registered under GST is authorised to charge

and collect GST on the sale of goods or services.2. Intra-state sales. Sales of goods and services within the same state (or Union Territory) are

called intra-state sales.3. Inter-state sales. Sales of goods and services outside the state (or Union Territory) are called

inter-state sales.4. Input GST and Output GST. GST is paid by dealers on purchase of goods and services

and is collected from customers on sale of goods and services. GST paid by a dealer is called Input GST and GST collected from a customer is called Output GST.

5. Types of taxes under GST. There are three taxes applicable under GST: (i) Central Goods and Services Tax (CGST). (ii) State Goods and Services Tax (SGST) or Union Territory Goods and Services Tax

(UTGST).Both these taxes are levied on intra-state sales i.e. on sales of goods and services

within the same state. In intra-state sales, GST is divided equally among Centre and State Governments.

For example, a dealer in Karnataka sells goods worth ` 3000 to a dealer (or consumer) in Karnataka. Suppose GST rate is 12% on these goods, then GST will comprise of CGST @ 6%

1 Goods and Services Tax

Commercial Mathematics

Understanding ICSE Mathematics – X2

and SGST @ 6%. The seller will collect 6% of ` 3000 i.e. ` 180 as CGST which will go to the Central Government and 6% of ` 3000 i.e. ` 180 which will go to the State Government of Karnataka. Thus the dealer collects 12% of ` 3000 i.e. ` 360 as total GST, half of which goes to the Central Government and the other half goes to the State Government of Karnataka.

(iii) Integrated Goods and Services Tax (IGST).IGST is levied on inter-state sales i.e. on sales of goods and services outside the state.

It is also levied on import of goods and services into India and on export of goods and services outside India. IGST goes to the Central Government.

For example, a dealer from Madhya Pradesh sells goods worth ` 50000 to a dealer in Punjab. Suppose GST rate is 18% on these goods, then the seller will collect 18% of ` 50000 i.e. ` 9000 as IGST and the entire amount of IGST will go to the Central Government.

1.1.2 gst rate structureGoods and Services are divided into five slabs for collection of GST. (i) Essential items including (unpacked) food 0% (ii) Common use items 5% (iii) Standard rate 12% (iv) Maximum goods and all services standard rate 18% (v) Luxury and sin (tobacco) items 28%

1.1.3 input gst credit or input tax credit (itc)Every dealer registered under GST is entitled to set off Input GST (i.e. GST paid) against output GST (i.e. GST collected) as follows:

Input GST Credit (ITC) Output GST

CGST Credit First CGST, then IGST

SGST/UTGST Credit First SGST/UTGST, then IGST

IGST Credit First IGST, second CGST, then SGST/UTGST

CGST credit cannot be set off against SGST/UTGST and vice-versa.

Both centre and states allow to set off Input GST against Output GST. Every dealer has to pay net GST (output GST – input GST) on the sale and purchase of goods and services.

1.1.4 gst value added taxEvery dealer pays GST on the purchases of goods and collects GST on the sale of goods and difference of the two i.e. GST collected – GST paid is payable to the Government. Thus, GST payable to the Government by a dealer = Output GST – input GST = GST on the sale price – GST on the purchase price = GST on (the sale price – the purchase price) = GST on value addition.

This means that GST is the only the value addition tax.

1.1.5 objectives and advantages of gst (i) Ease of doing business: GST harmonizes tax administration between the Centre and

States which will improve the ease of doing business. (ii) Reducing tax burden: GST aims at reducing burden of tax on the consumer. Earlier,

the manufacturer, the wholesaler, the retailer and the consumer, all had to pay taxes


at every stage of transaction. This used to create a cascading effect of tax on tax which was finally borne by the consumer. As GST is levied only on value addition, so it avoids cascading effect of tax and provides some relief to the consumer.

(iii) Reduce tax evasion: GST has e-compliance mechanism. Every tax payer registered under GST has to file GST return electronically for every transaction (purchase and sale) and will match input GST credit against output GST and pay net GST which will reduce tax evasion.

(iv) The tax system becomes more transparent, regular and predictable.

Illustrative Examples

Example 1. A consumer buys a refrigerator whose marked price is ` 36000 from a dealer at a discount of 15%. If the rate of GST is 18%, find

(i) the amount of tax (under GST) paid by the consumer for the purchase. (ii) the total amount that the consumer pays for the refrigerator.

Solution. Marked price of refrigerator = ` 36000, rate of discount = 15% Amount of discount = 15% of ` 36000 = ` 5400 Selling price = ` 36000 – ` 5400 = ` 30600 Rate of GST = 18%

(i) The amount of tax (under GST) paid by the consumer

= 18% of ` 30600 = ` ×18

10030600 = ` 5508.

(ii) The amount which the consumer pays for the refrigerator

= Cost of refrigerator to consumer + GST paid by consumer

= ` 30600 + ` 5508 = ` 36108

Example 2. A retailer buys an air-conditioner from a wholesaler for ` 35000 and sells it to a consumer at a profit of 8%. If the rate of GST is 28%, calculate the tax liability of the retailer.

Solution. For retailer:

Purchase price of air-conditioner = ` 35000, rate of GST = 28%

Amount of GST paid by the retailer to the wholesaler

= 28% of ` 35000 = ` ×28

10035000 = ` 9800

∴ Input GST of the retailer = ` 9800

The retailer sells the air-conditioner to a consumer at 8% profit,

profit of the retailer = 8% of ` 35000 = ` ×8

10035000 = ` 2800

Selling price of air-conditioner = C.P. + profit

= ` 35000 + ` 2800 = ` 37800.

Amount of GST collected by the retailer from the consumer

= 28% of ` 37800 = ` ×28

10037800 = ` 10584

∴ Output GST of retailer = ` 10584 Tax liability of the retailer = Output GST – input GST = ` 10584 – ` 9800 = ` 784.


Alternatvely

Tax liability of the retailer

= GST on value addition = GST on profit

= 28% of ` 2800 = ` ×28

1002800 = ` 784

Example 3. A manufacturer buys raw material worth ` 4000, paying GST at the rate of 5%. He sells the finished product to a shopkeeper at a profit of 30%. If the rate of GST for the finished product is 12%, find the tax liability of the manufacturer.

Solution. Value of raw material = ` 4000, rate of GST on raw material = 5%

Tax paid by the manufacturer for the raw material

= 5% of ` 4000 = ` ×5

1004000 = ` 200.

Input GST of the manufacturer = ` 200 Profit of the manufacturer = 30% of ` 4000

= ` ×30

1004000 = ` 1200

Selling price of the finished product = C.P. + profit

= ` 4000 + ` 1200 = ` 5200

Tax collected by the manufacturer from the shopkeeper for the finished product

= 12% of ` 5200

= ` ×12

1005200 = ` 624

Output GST of manufacturer = ` 624. Tax liability of the manufacturer = Output GST – input GST

= ` 624 – ` 200 = ` 424

Example 4. The marked price of an article is ` 3500. A dealer in Delhi sells the article to a consumer in the same city at a profit of 10%. If the rate of GST is 12%, find

(i) IGST, CGST and SGST paid by the dealer to the Central and State Governments. (ii) the amount which the consumer pays for the article.

Solution.

(i) Marked price of the article = ` 3500, profit = 10%

Selling price of the article = + 10

1001 of ` 3500

= ` 1110

3500×

= ` 3850

As the sale is in the same city, so this sale is intra-state. Rate of GST is 12%, it comprises of CGST at 6% and SGST at 6%. Amount of GST collected by the dealer from the consumer: IGST = Nil (Q sale is intra-state)

CGST = 6% of ` 3850 = ` ×6

1003850 = ` 231

SGST = 6% of ` 3850 = ` 231

Amount of tax paid by the dealer to the Central and State Governments: CGST = ` 231 to the Central Government and SGST = ` 231 to Delhi Government.


Example 5. Manufacturer A sells a washing machine to a dealer B for ` 12500. The dealer B sells it to a consumer at a profit of ` 1500. If the sales are intra-state and the rate of GST is 12%, find

(i) the amount of tax (under GST) paid by the dealer B to the Central Government.

(ii) the amount of tax (under GST) received by the State Government. (iii) the amount that the consumer pays for the machine.

Solution. As the sales are intra-state and the rate of GST is 12%, so GST comprises of 6% as CGST and 6% as SGST. Manufacturer A sells the washing machine to dealer B for ` 12500, amount of GST collected by manufacturer A from dealer B (or paid by dealer B to A):

CGST = 6% of ` 12500 = ` 6

100×

12500 = ` 750,

SGST = 6% of ` 12500 = ` 6

100×

12500 = ` 750.

∴ Amount of input GST of dealer B:

input CGST = ̀ 750, input SGST = ` 750.

Manufacturer A will pay ̀ 750 as CGST and ` 750 as SGST.

Since the dealer B sells the washing machine to a consumer at a profit of ` 1500, the selling price of machine by dealer B (or cost price of machine to the consumer)

= ` 12500 + ` 1500 = ` 14000.

The amount of GST collected by dealer B (or paid by consumer):

CGST = 6% of ` 14000 = ` 6

10014000×

= ` 840,

SGST = 6% of ` 14000 = ` 6

10014000×

= ` 840.

∴ Amount of output GST of dealer B:

output CGST = ̀ 840, output SGST = ` 840.

(i) Amount of tax (under GST) paid by dealer B to the Central Government

= CGST paid by dealer B to the Central Government

= Output CGST – input CGST

= ` 840 – ` 750 = ` 90.

(ii) Amount of SGST paid by dealer B = Output SGST – input SGST

= ` 840 – ` 750 = ` 90

Amount of tax (under GST) received by the State Government

= SGST paid by dealer A + SGST paid by dealer B

= ` 750 + ` 90 = ` 840.

(iii) The amount which the consumer pays for the machine

= Cost price of machine to consumer + GST paid by consumer

= ` 14000 + CGST paid by consumer + SGST paid by consumer

= ` 14000 + ` 840 + ` 840 = ` 15680.

Example 6. A shopkeeper buys an article whose printed price is ` 4000 from a wholesaler at a discount of 20% and sells it to a consumer at the printed price. If the sales are intra-state and the rate of GST is 12%, find

(i) the price of the article inclusive of GST at which the shopkeeper bought it.


(ii) the amount of tax (under GST) paid by the shopkeeper to the State Government. (iii) the amount of tax (under GST) received by the Central Government. (iv) the amount which the consumer pays for the article.

Solution. As the sales are intra-state and the rate of GST is 12%, so GST comprises of CGST at 6% and SGST at 6%.

(i) Printed price = ` 4000, rate of discount = 20%.

Amount of discount = 20% of ` 4000 = ` 20

1004000×

= ` 800.

∴ The price of the article which the shopkeeper paid to the wholesaler

= ` 4000 – ` 800 = ` 3200.

Amount of GST paid by the shopkeeper to the wholesaler:

CGST = 6% of ` 3200 = ` 6

1003200×

= ` 192.

SGST = 6% of ` 3200 = ` 192.

∴ The price of the article inclusive of GST at which the shopkeeper bought it

= ` 3200 + ` 192 + ` 192 = ` 3584.

(ii) The wholesaler will pay ` 192 as CGST to the Central Government and ` 192 as SGST to the State Government.

Amount of input GST of the shopkeeper:

CGST = ` 192; SGST = ` 192.

The shopkeeper sells the article to a consumer at printed price of ` 4000.

Amount of GST collected by the shopkeeper (or paid by consumer):

CGST = 6% of ` 4000 = ` 6

1004000×

= ` 240,

SGST = 6% of ` 4000 = ` 240.

Amount of output GST of the shopkeeper:

CGST = ` 240; SGST = ` 240

Amount of tax (under GST) paid by the shopkeeper to the State Government = SGST paid by the shopkeeper to the State Government = Output SGST – input SGST = ` 240 – ` 192 = ` 48.

(iii) Amount of CGST paid by the shopkeeper = Output CGST – input CGST = ` 240 – ` 192 = ` 48. The amount of tax (under GST) received by the Central Government = CGST paid by wholesaler + CGST paid by shopkeeper = ` 192 + ` 48 = ` 240. (iv) The amount which the consumer pays for the article = Cost price of article to consumer + GST paid by consumer = ` 4000 + CGST paid by consumer + SGST paid by consumer = ` 4000 + ` 240 + ` 240 = ` 4480.

Example 7. The printed price of an air-conditioner (AC) is ` 45000. The wholesaler allows a discount of 10% to a dealer. The dealer sells the air-conditioner to a consumer at a discount of 4% on the marked price. If the sales are intra-state and rate of GST is 18%, find:


(i) the amount of tax (under GST) paid by the dealer to Central and State Governments.

(ii) the amount of tax (under GST) received by Central and State Governments. (iii) the total amount (inclusive of tax) paid by the consumer for the air-conditioner.

Solution. As all the sales are intra-state and the rate of GST is 18%, so GST comprises of CGST at 9% and SGST at 9%.

(i) As the wholesaler sells the air-conditioner to a dealer at a discount of 10%,

the selling price of the air-conditioner by the wholesaler (excluding tax)

= ` 1 10100

−

× 45000 = `

9

10045000×

= ` 40500.

∴ Cost price of AC to the dealer (excluding tax) = ` 40500.

Amount of GST collected by the wholesaler (or paid by dealer to wholesaler):

CGST = 9% of ` 40500 = ` 9

10040500×

= ` 3645;

SGST = 9% of ` 40500 = ` 3645.

∴ The wholesaler will pay ` 3645 as CGST to the Central Government and ` 3645 as SGST to the State Government.

Amount of input GST of the dealer:

CGST = ` 3645; SGST = ` 3645.

As the dealer sells the air-conditioner to a consumer at a discount of 4% on the marked price, the selling price of the air-conditioner by the dealer (excluding tax)

= ` 1 4100

−

× 45000 = `

2425

45000×

= ` 43200.

∴ Cost price of AC to the consumer (excluding tax) = ` 43200.

Amount of GST collected by the dealer (or paid by consumer):

CGST = 9% of ` 43200 = ` 9100

43200×

= ` 3888;

SGST = 9% of ` 43200 = ` 3888.

Amount of output GST of the dealer:

CGST = ` 3888, SGST = ` 3888.

Amount of tax (under GST) paid by dealer to the Central Government


= ` 3888 – ` 3645 = ` 243

Amount of tax (under GST) paid by dealer to the State Government

= Output SGST – input SGST

= ` 3888 – ` 3645 = ` 243.

(ii) The amount of tax (under GST) received by the Central Government

= CGST paid by wholesaler + CGST paid by dealer

= ` 3645 + ` 243 = ` 3888

The amount of tax (under GST) received by the State Government

= SGST paid by wholesaler + SGST paid by dealer

= ` 3645 + ` 243 = ` 3888


(iii) The total amount (inclusive of tax) paid by the consumer for the air-conditioner

= Cost of AC + GST paid by consumer


= ` 43200 + ` 3888 + ` 3888 = ` 50976.

Example 8. A retailer buys a TV from a manufacturer for ` 25000. He marks the price of the TV 20% above his cost price and sells it to a consumer at 10% discount on the marked price. If the sales are intra-state and rate of GST is 12%, find:

(i) the marked price of the TV. (ii) Consumer’s cost price of TV inclusive of tax (under GST). (iii) GST paid by the retailer to the Central and State Governments.

Solution. The cost price of the TV which the retailer pays to the manufacturer = ` 25000

(i) As the retailer marks the price of TV 20% above his cost price,

∴ the marked price of the TV = ` 120

100+

× 25000.

= ` 120100

×

25000 = ` 30000.

(ii) As the sales are intra-state and the rate of GST is 12%, so GST comprises of CGST at 6% and SGST at 6%.

As the retailer sells the TV to a consumer at 10% discount on the marked price, selling price of the TV by the retailer

= ` 1−

10100 × 30000 = `

910

×

30000 = ` 27000.

Amount of GST collected by retailer from consumer (or paid by consumer to retailer):

CGST = 6% of ` 27000 = ` 6

100×

27000 = ` 1620,

SGST = 6% of ` 27000 = ` 1620.

∴ Consumer's cost price of TV inclusive of tax (under GST)

= Cost price of TV to consumer + GST paid by consumer


= ` 27000 + ` 1620 + ` 1620

= ` 30240.

(iii) Amount of GST collected by manufacturer from retailer:

CGST = 6% of ` 25000 = ` 6

100×

25000 = ` 1500,

SGST = 6% of ` 25000 = ` 1500.

Amount of input GST of the retailer:

CGST = ` 1500, SGST = ` 1500

Amount of output GST of the retailer:

CGST = ` 1620, SGST = ` 1620

GST paid by the retailer to the Central Government


= ` 1620 – ` 1500 = ` 120


GST paid by the retailer to the State Government


= ` 1620 – ` 1500 = ` 120

∴ Total GST paid by the retailer to the Central and State Governments

= ` 120 + ` 120 = ` 240.

Example 9. The printed price of a carpet is ` 2500. A wholesaler in West Bengal buys the carpet from a manufacturer in Maharashtra at a discount of 12% on the printed price. The wholesaler sells the carpet to a retailer in Bihar at 32% above the marked price. If the rate of GST on the carpet is 5%, find:

(i) the price inclusive of tax (under GST) at which the wholesaler bought the carpet.

(ii) the price inclusive of tax (under GST) at which the retailer bought the carpet. (iii) the tax (under GST) paid by the wholesaler to the Government. (iv) the tax (under GST) received by the Central Government.

Solution. The printed price of the carpet is ` 2500. The rate of GST on the sale or purchase of the carpet is 5%. Here both the given sales from manufacturer to wholesaler and wholesaler to retailer are inter-state, so IGST is levied on these sales at 5%.

(i) As the wholesaler buys the carpet from a manufacturer at 12% discount on the printed price,

∴ cost price of the carpet to the wholesaler

= ` 1−

12100

× 2500 = ` 2225

2500×

= ` 2200.

Amount of IGST collected by manufacturer from wholesaler (or paid by wholesaler

to manufacturer)

= 5% of ` 2200 = ` 5100

×

2200 = ` 110.

The price inclusive of tax (under GST) at which the wholesaler bought the carpet

= Cost of carpet to wholesaler + IGST paid by wholesaler

= ` 2200 + ` 110 = ` 2310.

The manufacturer will pay ` 110 as IGST to the Central Government.

Input IGST of the wholesaler = ` 110.

(ii) As the wholesaler sells the carpet to a retailer at 32% above the marked price,

the selling price of the carpet by the wholesaler

= ` 1+

32100

× 2500 = ` 3325

×

2500 = ` 3300.

∴ Cost price (excluding tax) of the carpet to the retailer = ` 3300.

Amount of IGST collected by wholesaler from retailer (or paid by retailer to

wholesaler)

= 5% of ` 3300 = ` 5100

×

3300 = ` 165.

The price inclusive of tax (under GST) at which the retailer bought the carpet

= Cost of carpet to retailer + IGST paid by retailer

= ` 3300 + ` 165 = ` 3465.


(iii) Output IGST of the wholesaler = ` 165.

The tax (under GST) paid by the wholesaler to the Central Government

= Output IGST – input IGST

= ` 165 – ` 110 = ` 55.

(iv) The tax (under GST) received by the Central Government

= IGST received from manufacturer + IGST received from wholesaler

= ` 110 + ` 55 = ` 165.

NoteNone of the State Governments (Maharashtra or West Bengal or Bihar) gets any tax (under GST) on the above said sales of the carpet. The whole tax (under GST) on the sales of the carpet goes to the Central Government.

Example 10. A dealer in U.P. buys an article for ` 30000 from a wholesaler in U.P. He sells the article to a consumer in Gujarat at a profit of 8%. If the rate of GST is 12%, find

(i) the tax (under GST) paid by the wholesaler to Governments. (ii) the tax (under GST) paid by the dealer to the Governments. (iii) the amount which the consumer pays for the article.

Solution. (i) As the dealer in U.P. buys an article for ` 30000 from a wholesaler in U.P., so this sale is intra-state.

Rate of GST is 12%, so GST comprises of CGST at 6% and SGST at 6%.

Tax (under GST) collected by the wholesaler from the dealer:

CGST = 6% of ` 30000 = ` ×6

10030000 = ` 1800,

SGST = 6% of ` 30000 = ` 1800

Amount of tax (under GST) paid by the wholesaler: ` 1800 as CGST to the Central Government and ` 1800 as SGST to the State Government of U.P. (ii) The dealer sells the article to a consumer in Gujarat, so this sale is inter-state. Rate

of GST is 12%. On this sale, IGST is levied at 12%.

Profit of the dealer = 8% of ` 30000

= ` ×8

10030000 = ` 2400.

Selling price of the article by the dealer = C.P. + Profit

= ` 30000 + ` 2400 = ` 32400.

IGST collected by the dealer from the consumer

= 12% of ` 32400 = ` ×12

10032400 = ` 3888.

Output IGST of the dealer = ` 3888 Tax (under GST) paid by the dealer to the Government = Output IGST – (input CGST + input SGST) = ` 3880 – (` 1800 + ` 1800) = ` 288 Tax paid by the dealer to the Central Government = ` 288. No tax is paid by the dealer to the State Government of U.P. (iii) The amount which the consumer pays for the article = C.P. to consumer + IGST paid by consumer

= ` 32400 + ` 3888 = ` 36288.


Example 11. A shopkeeper in Rajasthan buys an article at the printed price of ` 40000 from a wholesaler in Delhi. The shopkeeper sells the article to a consumer in Rajasthan at a profit of 25% on the basic cost price. If the rate of GST is 18%, find

(i) the price of the article inclusive of tax (under GST) at which the shopkeeper bought it.

(ii) the amount of tax (under GST) paid by the shopkeeper to Government. (iii) the amount of tax (under GST) received by Delhi Government. (iv) the amount of tax (under GST) received by Central Government. (v) the amount which the consumer pays for the article.

Solution. (i) As the shopkeeper in Rajasthan buys an article for ` 40000 from a wholesaler in Delhi, so this sale is inter-state.

Rate of GST is 18%. On this sale IGST is levied at 18%.

IGST collected by wholesaler from shopkeeper

= 18% of ` 40000 = ` 18100

×

40000 = ` 7200.

∴ The price of the article inclusive of tax (under GST) at which the shopkeeper bought it

= Cost price of article to shopkeeper + GST paid by the shopkeeper

= ` 40000 + IGST paid by shopkeeper to wholesaler

= ` 40000 + ` 7200 = ` 47200.

(ii) The wholesaler will pay ` 7200 as IGST to the Central Government.

The amount of input IGST of the shopkeeper = ` 7200.

The shopkeeper sells the article to a consumer at a profit of 25% on the basic cost price,

the selling price of article by the shopkeeper

= ` 1+

25100

× 40000 = ` 54×

40000 = ` 50000.

As the shopkeeper sells the article to a consumer in Rajasthan, so this sale is intra-state.

∴ GST comprises of CGST at 9% and SGST at 9%.

Amount of GST collected by shopkeeper from consumer:

CGST = 9% of ` 50000 = ` 4500,

SGST = 9% of ` 50000 = ` 4500.

Amount of output GST of the shopkeeper:

CGST = ` 4500, SGST = ̀ 4500.

Amount of tax (under GST) paid by the shopkeeper to Government:

First set off ` 4500 input IGST against ` 4500 output CGST.

Then set off the balance ` 2700 (` 7200 – ` 4500) input IGST against output SGST

∴ SGST paid by the shopkeeper to the State Government (Rajasthan)

= Output SGST – balance of input IGST

= ` 4500 – ` 2700 = ` 1800.


∴ Net tax (under GST) paid by shopkeeper to Government:

No tax is paid to the Central Government

Tax paid to Rajasthan Government = ` 1800.

(iii) Amount of tax (under GST) received by Delhi Government is NIL.

(iv) Amount of tax (under GST) received by the Central Government

= IGST received from wholesaler + CGST received from shopkeeper

= ` 7200 + NIL = ` 7200

(v) The amount which the consumer pays for the article

= Cost price to consumer + GST paid by consumer


= ` 50000 + ` 4500 + ` 4500 = ` 59000.

Example 12. Akash (in Bihar) buys an article for ` 20000. He sells it to Sanjeev (in Bihar) at a profit of 10%. Sanjeev sells the article to Rehman (in Odisha) at a profit of 15%. If the rate of GST on the article is 18%, find the tax (under GST) paid by Sanjeev to the Government.

Solution. Akash (in Bihar) sells the article to Sanjeev (in Bihar), so this sale is intra-state. Rate of GST is 18%, so GST comprises of CGST at 9% and SGST at 9%.

Profit of Akash = 10% of ` 20000 = ` 2000.

S.P. of the article by Akash = C.P. + Profit

= ` 20000 + ` 2000 = ` 22000

Tax (under GST) collected by Akash from Sanjeev:

CGST = 9% of ` 22000 = ` 1980,

SGST = 9% of ` 22000 = ` 1980,

input CGST of Sanjeev = ` 1980,

input SGST of Sanjeev = ` 1980.

Sanjeev sells the article to Rehman (in Odisha), so this sale is inter-state. IGST is levied at 18%.

Profit of Sanjeev = 15% of ` 22000 = ` 3300

S.P. of the article by Sanjeev = ` 22000 + ` 3300 = ` 25300

IGST collected by Sanjeev from Rehman

= 18% of ` 25300 = ` 4554

Output IGST of Sanjeev = ` 4554.

Tax (under GST) paid by Sanjeev to the Government

= Output IGST – (input CGST + input SGST)

= ` 4554 – (` 1980 + ` 1980) = ` 594

Tax (under GST) paid by Sanjeev to the Central Government = ` 594

Example 13. Ms. Chawla goes to a shop to buy a leather coat which costs ` 885 (list price). The rate of GST is 18%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ` 885, inclusive of GST. Find the reduction needed in the price of the coat.

Solution. Let the reduced price of the leather coat be ` x.

Amount of GST on `x = 18% of `x = ` 18100x.


∴ The amount to be paid by Ms. Chawla for the coat

= `x + `18100x = ` 1+

18100

x = `5950 x

According to given, 5950 x = 885

⇒ x = 5059

× 885 = 50 × 15 = 750.

∴ The reduced price of the leather coat = ` 750.

Hence, the reduction needed in the price of coat = ` 885 – ` 750 = ` 135.

NoteIf nothing is mentioned about sale (intra-state or inter-state), we shall take the sale to be an intra-state sale.

Example 14. The price of a bicycle is ` 3136 inclusive of tax (under GST) at the rate of 12% on its listed price. A buyer asks for a discount on the listed price so that after charging GST, the selling price becomes equal to the listed price. Find the amount of discount which the seller has to allow for the deal.

Solution. Let the listed price of the bicycle be ` P.

Amount of GST on ` P = 12% of ` P = ` 325 P.

Selling price of the bicycle including tax = ` P + `325 P = ` 28

25 P.

According to given, 2825

P = 3136

⇒ P = 2528

× 3136 = 25 × 112 = 2800.

∴ The list price of the bicycle = ` 2800.

Let the amount of discount be ` x.

∴ The reduced price of the bicycle = ̀ (2800 – x).

Amount of GST on ` (2800 – x) = 12% of ` (2800 – x)

= ` 12

100 × (2800 – x) = `325 (2800 – x)

∴ New selling price of the bicycle including GST

= ` (2800 – x) + `325 (2800 – x) = ̀

2825

(2800 – x).


(2800 – x) = 2800

⇒ 2800 – x = 2500 ⇒ x = 300.

∴ The amount of discount = ` 300.

Example 15. A shopkeeper buys an article whose list price is ` 4500 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price and charges GST at the rate of 12%. If the sales are intra-state and the shopkeeper has to pay tax (under GST) of ` 27, to the State Government, find the rate of discount at which he bought the article from the wholesaler.

Solution. The sales are intra-state and the rate of GST is 12%, so GST comprises of CGST at 6% and SGST at 6%.

Let the amount of discount be `x.

Selling price of the article (excluding tax) by the wholesaler

= listed price – discount = ` (4500 – x).


Amount of GST collected by the wholesaler from the shopkeeper:

CGST = 6% of ` (4500 – x) = ` 6

100× −

( )4500 x

= ` 270 −

350

x ,

SGST = 6% of ` (4500 – x) = ` 270 −

350

x

Input GST of shopkeeper:

Input CGST = ` 270 −

350

x , input SGST = ` 270 −

350

x

The shopkeeper sells the article to a consumer at the list price i.e. for ` 4500.

Amount of GST collected by the shopkeeper from the consumer:

CGST = 6% of ` 4500 = ` 6

100×

4500 = ` 270,

SGST = 6% of ` 4500 = ` 270.

Output GST of shopkeeper:

Output CGST = ` 270, output SGST = ` 270.

∴ The amount of tax (under GST) paid by the shopkeeper to the State Government


= ` 270 – ` 270 −

350

x = ` 350

x.


x = 27 ⇒ x = 450.

∴ The amount of discount = ` 450.

Thus, the shopkeeper gets a discount of ` 450 from the wholesaler.

∴ Rate of discount = amount of discountprice of article

100printed

×

%

= 4504500

×

100 % = 10%

Example 16. A shopkeeper sells an article at the listed price of ` 1500. The rate of GST on the article is 18%. If the sales are intra-state and the shopkeeper pays a tax (under GST) of ` 27 to the Central Government, find the amount inclusive of tax at which the shopkeeper purchased the article from the wholesaler.

Solution. Sales are intra-state and the rate of GST is 18%, so GST comprises of CGST at 9% and SGST at 9%.

Let the shopkeeper buy the article from the wholesaler for `x (excluding tax).

Amount of GST paid by the shopkeeper to wholesaler:

CGST = 9% of ` x = ` 9

100x ,

SGST = 9% of ` x = ` 9

100x .

∴ Input CGST of the shopkeeper = ` 9

100x .

The shopkeeper sells the article at the list price of ` 1500.

Amount of GST collected by the shopkeeper:

CGST = 9% of `1500 = `9

100×

1500 = `135,

SGST = 9% of `1500 = `135.


∴ Output CGST of the shopkeeper = ` 135

The amount of tax (under GST) paid by the shopkeeper to the Central Government


= ` 135 – ` 9

100x = ` 135 −

9100

x .

According to given, 135 – 9

100x = 27

⇒ 9

100x = 108 ⇒ x = 1200.

Thus, the shopkeeper purchased the article from the wholesaler for `1200.

CGST = 9% of `1200 = `108,

SGST = 9% of `1200 = `108.

∴ The amount inclusive of tax (under GST) at which the shopkeeper purchased the article from the wholesaler

= Cost of the article to the shopkeeper + GST paid by the shopkeeper

= `1200 + `108 + `108 = `1416.

Exercise 1

1. An article is marked at ` 15000. A dealer sells it to a consumer at 10% profit. If the rate of GST is 12%, find:

(i) the selling price (excluding tax) of the article. (ii) the amount of tax (under GST) paid by the consumer. (iii) the total amount paid by the consumer.

2. A shopkeeper buy goods worth ` 4000 and sells these at a profit of 20% to a consumer in the same state. If GST is charged at 5%, find:

(i) the selling price (excluding tax) of the goods. (ii) CGST paid by the consumer. (iii) SGST paid by the consumer. (iv) the total amount paid by the consumer.

3. The marked price of an article is ` 12500. A dealer in Kolkata sells the article to a consumer in the same city at a profit of 8%. If the rate of GST is 18%, find

(i) the selling price (excluding tax) of the article. (ii) IGST, CGST and SGST paid by the dealer to the Central and State Governments. (iii) the amount which the consumer pays for the article.

4. A shopkeeper buys an article from a wholesaler for ` 20000 and sells it to a consumer at 10% profit. If the rate of GST is 12%, find the tax liability of the shopkeeper.

5. A dealer buys an article for ` 6000 from a wholesaler. The dealer sells the article to a consumer at 15% profit. If the sales are intra-state and the rate of GST is 18%, find

(i) input CGST and input SGST paid by the dealer. (ii) output CGST and output SGST collected by the dealer. (iii) the net CGST and SGST paid by the dealer. (iv) the total amount paid by the consumer.

6. A manufacturer buys raw material worth ` 7500 paying GST at the rate of 5%. He sells the finished product to a dealer at 40% profit. If the purchase and the sale both are intra-state and the rate of GST for the finished product is 12%, find:


(i) the input tax (under GST) paid by the manufacturer. (ii) the output tax (under GST) collected by the manufacturer. (iii) the tax (under GST) paid by the manufacturer to the Central and State

Governments. (iv) the amount paid by the dealer for the finished product.

7. A manufacturer sells a T.V. to a dealer for ` 18000 and the dealer sells it to a consumer at a profit of ` 1500. If the sales are intra-state and the rate of GST is 12%, find:

(i) the amount of GST paid by the dealer to the State Government. (ii) the amount of GST received by the Central Government. (iii) the amount of GST received by the State Government. (ivii) the amount that the consumer pays for the T.V.

8. A shopkeeper buys a camera at a discount of 20% from a wholesaler, the printed price of the camera being `1600. The shopkeeper sells it to a consumer at the printed price. If the sales are intra-state and the rate of GST is 12%, find:

(i) GST paid by the shopkeeper to the Central Government. (ii) GST received by the Central Government. (iii) GST received by the State Government. (iv) the amount at which the consumer bought the camera.

9. A dealer buys an article at a discount of 30% from the wholesaler, the marked price being `6000. The dealer sells it to a consumer at a discount of 10% on the marked price. If the sales are intra-state and the rate of GST is 5%, find:

(i) the amount paid by the consumer for the article. (ii) the tax (under GST) paid by the dealer to the State Government. (iii) the amount of tax (under GST) received by the Central Government.

10. The printed price of an article is ` 50000. The wholesaler allows a discount of 10% to a shopkeeper. The shopkeeper sells the article to a consumer at 4% above the marked price. If the sales are intra-state and the rate of GST is 18%, find:

(i) the amount inclusive of tax (under GST) which the shopkeeper pays for the article.

(ii) the amount paid by the consumer for the article. (iii) the amount of tax (under GST) paid by the shopkeeper to the Central Government. (iv) the amount of tax (under GST) received by the State Government.

11. A retailer buys a T.V. from a wholesaler for `40000. He marks the price of the T.V. 15% above his cost price and sells it to a consumer at 5% discount on the marked price. If the sales are intra-state and the rate of GST is 12%, find:

(i) the marked price of the T.V. (ii) the amount which the consumer pays for the T.V. (iii) the amount of tax (under GST) paid by the retailer to the Central Government. (iv) the amount of tax (under GST) received by the State Government.

12. A shopkeeper buys an article from a manufacturer for `12000 and marks up it price by 25%. The shopkeeper gives a discount of 10% on the marked up price and he gives a further off-season discount of 5% on the balance to a customer of T.V. If the sales are intra-state and the rate of GST is 12%, find:

(i) the price inclusive of tax (under GST) which the consumer pays for the T.V. (ii) the amount of tax (under GST) paid by the shopkeeper to the State Government. (iii) the amount of tax (under GST) received by the Central Government.


13. The printed price of an article is `40000. A wholesaler in Uttar Pradesh buys the article from a manufacturer in Gujarat at a discount of 10% on the printed price. The wholesaler sells the article to a retailer in Himachal at 5% above the printed price. If the rate of GST on the article is 18%, find:

(i) the amount inclusive of tax (under GST) paid by the wholesaler for the article. (ii) the amount inclusive of tax (under GST) paid by the retailer for the article. (iii) the amount of tax (under GST) paid by the wholesaler to the Central Government. (iv) the amount of tax (under GST) received by the Central Government.

14. A dealer in Delhi buys an article for ` 16000 from a wholesaler in Delhi. He sells the article to a consumer in Rajasthan at a profit of 25%. If the rate of GST is 5%, find:

(i) the tax (under GST) paid by the wholesaler to Governments. (ii) the tax (under GST) paid by the dealer to the Government. (iii) the amount which the consumer pay for the article.

15. A shopkeeper in Delhi buys an article at the printed price of ` 24000 from a wholesaler in Mumbai. The shopkeeper sells the article to a consumer in Delhi at a profit of 15% on the basic cost price. If the rate of GST is 12%, find:

(i) the price inclusive of tax (under GST) at which the shopkeeper bought the article. (ii) the amount which the consumer pays for the article. (iii) the amount of tax (under GST) received by the State Government of Delhi. (iv) the amount of tax (under GST) received by the Central Government.

16. A dealer in Maharashtra buys an article from a wholesaler in Maharashtra at a discount of 25%, the printed price of the article being ` 20000. He sells the article to a consumer in Telengana at a discount of 10%. on the printed price. If the rate of GST is 12, find:

(i) the tax (under GST) paid by the wholesaler to Governments. (ii) the tax (under GST) paid by the dealer to the Government. (iii) the amount which the consumer pays for the article.

17. Kiran purchases an article for ` 5310 which includes 10% rebate on the marked price and 18% tax (under GST) on the remaining price. Find the marked price of the article.

18. A shopkeeper buys an article whose list price is ` 8000 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price. The sales are intra-state and the rate of GST is 18%. If the shopkeeper pay a tax (under GST) of ` 72 to the State Government, find the rate of discount at which he bought the article from the wholesaler.

Multiple Choice QuestionsA retailer purchases a fan for ` 1500 from a wholesaler and sells it to a consumer at 10% profit. If the sales are intra-state and the rate of GST is 12%, then choose the correct answer from the given four options for questions 1 to 6:

1. The selling price of the fan by the retailer (excluding tax) is (a) ` 1500 (b) ` 1650 (c) ` 1848 (d) ` 1800

2. The selling price of the fan including tax (under GST) by the retailer is (a) ` 1650 (b) ` 1800 (c) ` 1848 (d) ` 18303. The tax (under GST) paid by the wholesaler to the Central Government is (a) ` 90 (b) ` 9 (c) ` 99 (d) ` 1804. The tax (under GST) paid by the retailer to the State Government is (a) ` 99 (b) ` 9 (c) ` 18 (d) ` 198


5. The tax (under GST) received by the Central Government is (a) ` 18 (b) ` 198 (c) ` 90 (d) ` 996. The cost of the fan to the consumer inclusive of tax is (a) ` 1650 (b) ` 1800 (c) ` 1830 (d) ` 1848

A shopkeeper bought a TV from a distributor at a discount of 25% of the listed price of ` 32000. The shopkeeper sells the TV to a consumer at the listed price. If the sales are intra-state and the rate of GST is 18%, then choose the correct answer from the given four options for questions 7 to 11:

7. The selling price of the TV including tax (under GST) by the distributor is (a) ` 32000 (b) ` 24000 (c) ` 28320 (d) ` 26160

8. The tax (under GST) paid by the distributor to the State Government is (a) ` 4320 (b) ` 2160 (c) ` 2880 (d) ` 720

9. The tax (under GST) paid by the shopkeeper to the Central Government is (a) ` 720 (b) ` 1440 (c) ` 2880 (d) ` 2160

10. The tax (under GST) received by the State Government is (a) ` 5760 (b) ` 4320 (c) ` 1440 (d) ` 2880

11. The price including tax (under GST) of the TV paid by the consumer is (a) ` 28320 (b) ` 37760 (c) ` 34880 (d) ` 32000

Summary Goods and Services Tax (abbreviated ‘GST’) is an indirect tax levied on the supply of

goods and services i.e. on the sale of goods and rendering services. Some terms related to GST 1. Dealer. Any person who buys goods or services for resale is known as a dealer (or trader).

A dealer can be a firm or a company. 2. Intra-state sales. Sales of goods and services within the same state (or Union Territory) are

called intra-state sales. 3. Inter-state sales. Sales of goods and services outside the state (or Union Territory) are called

inter-state sales. 4. Input GST and Output GST. GST is paid by dealers on purchase of goods and services

and is collected from customers on sale of goods and services. GST paid by a dealer is called Input GST and GST collected from a customer is called Output GST.

5. Types of taxes under GST. There are three taxes applicable under GST. (i) Central Goods and Services Tax (CGST) (ii) State Goods and Services Tax (SGST) or Union Territory Goods and Services

Tax (UTGST). Both these taxes are levied on intra-state sales. In intra-state sales GST is divided equally

among Centre and State Governments. For example, if rate of GST is 12% then GST comprises of CGST at 6% and SGST at

6%. (iii) Integrated Goods and Services Tax (IGST) IGST is levied on inter-state sales. It is also levied on import of goods and services

into India and on export of goods and services from India. IGST goes to the Central Government. Rate of IGST is same as rate of GST. If rate of GST is 18%, then IGST is also at the rate of 18%.


Input GST Credit Every dealer registered under GST is entitled to set off Input GST (i.e. GST paid) against

output GST (i.e. GST collected) as follows:

Input GST Credit (ITC) Output GSTCGST Credit First CGST, then IGSTSGST Credit First SGST, then IGSTIGST Credit First IGST, second CGST, then SGSTCGST credit cannot be set off against SGST and vice-versa.

Chapter Test

1. A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being ` 18000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the sales are intra-state and the rate of GST is 12%, find:

(i) the price inclusive of tax (under GST) at which the shopkeeper bought the machine. (ii) the price which the consumer pays for the machine. (iii) the tax (under GST) paid by the wholesaler to the State Government. (iv) the tax (under GST) paid by the shopkeeper to the State Government. (v) the tax (under GST) received by the Central Government.

2. A manufacturer listed the price of his goods at ` 1600 per article. He allowed a discount of 25% to a wholesaler who in turn allowed a discount of 20% on the listed price to a retailer. The retailer sells one article to a consumer at a discount of 5% on the listed price. If all the sales are intra-state and the rate of GST is 5%, find:

(i) the price per article inclusive of tax (under GST) which the wholesaler pays. (ii) the price per article inclusive of tax (under GST) which the retailer pays. (iii) the amount which the consumer pays for the article. (iv) the tax (under GST) paid by the wholesaler to the State Government for the article. (v) the tax (under GST) paid by the retailer to the Central Government for the article. (vi) the tax (under GST) received by the State Government.

3. Mukerjee purchased a movie camera for ` 25488, which includes 10% rebate on the list price and 18% tax (under GST) on the remaining price. Find the marked price of the camera.

4. The marked price of an article is ` 7500. A shopkeeper buys the article from a wholesaler at some discount and sells it to a consumer at the marked price. The sales are intra-state and the rate of GST is 12%. If the shopkeeper pays ` 90 as tax (under GST) to the State Government, find:

(i) the amount of discount. (ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid

to the wholesaler.

5. A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10% on the printed price but due to competition in the market, he allows a discount of 5% on the marked price to a buyer. If the rate of GST is 12% and the buyer pays ` 468∙16 for the article inclusive of tax (under GST), find

(i) the printed price of the article. (ii) the profit percentage of the retailer.


introductionIn ancient times, the rich and powerful persons who could defend themselves and their property used to keep the savings and valuables (ornaments) of the common people and charged some money for rendering this service. With the passage of time, it was realised that the deposited money could be used to lend to the needy persons as all the depositors do not withdraw their money at the same time. In due course of time, the moneylenders (rich persons) started paying some nominal rate of interest to the depositors and charging very high rate of interest from the borrowers. In this way they made huge profits by utilising the deposits of the common people. To keep the savings of the people in safe custody, banks came into existence.

A bank is an institution which mainly carries on the business of getting deposits and lending money.

The rate of interest which a bank charges from the borrowers is usually higher than the one it pays to the depositors. Now-a-days, apart from the business of taking deposits and lending money, many other financial transactions are also carried by banks.

Some functions of banks are given below : (i) getting deposits. (ii) lending money. (iii) transferring money from one place to another. (iv) providing traveller cheques and foreign exchange to the tourists. (v) renting deposit vaults (lockers) to keep valuables in safe custody. (vi) accepting payments for public utility services such as electricity bills, water bills,

phone bills, house tax, sales tax, income tax, salaries of employees etc.

different types of bank accountsThe banks offer different schemes under which we can open our accounts. Mainly, the four different types of bank accounts offered by a bank are : (i) Savings Bank Account. (ii) Current Bank Account. (iii) Fixed Deposit Account. (iv) Recurring (or cumulative) Deposit Account.

In this chapter, we shall be dealing only with the recurring (or cumulative) deposit account. We shall learn the computation of interest and maturity value (abbreviated ‘MV’) by using the formula:

I (interest) = P × ( 1)2 12 100

n n r+×

× and

MV (maturity value) = P × n + I.

2 Banking

Banking 21

2.1 recurring (or cumulative) deposit accountTo boost the savings among the people of small and middle income groups, there are recurring (or cumulative) time deposit schemes in banks and post offices. Under this scheme, an investor deposits a fixed amount (in multiples of ` 5) every month for a specified number of months (usually, in multiples of 3) and on expiry of this period (called maturity period), he gets the amount deposited by him together with the interest (usually, compounded quarterly at a fixed rate) due to him. The amount received by the investor on the expiry of the specified period is called maturity value.

The rate of interest is revised from time to time.

2.1.1 calculation of interest on recurring depositCalculation of interest on a recurring deposit using compound interest is cumbersome and time consuming work. However, we shall calculate interest on recurring deposit using simple interest.

NoteIf n is a natural number, then

1 + 2 + 3 + … + n = n(n 1)2+ …(i)

For example,

1 + 2 + 3 + … + 30 = 30(30 1)2+ = 15 × 31 = 465.

2.1.2 to find equivalent principal for one month for the whole depositSuppose a man deposits ` 250 per month in a recurring deposit for one year. Clearly in this recurring deposit, the amount deposited in the first month (` 250) will remain with the bank for 12 months i.e. it (` 250) will earn interest for 12 months. The amount deposited in the 2nd month will earn interest for 11 months and so on.

Thus, ` 250 for 12 months = ` (250 × 12) for one month ` 250 for 11 months = ` (250 × 11) for one month ` 250 for 10 months = ` (250 × 10) for one month ` 250 for 19 months = ` (250 × 19) for one month ` 250 for 18 months = ` (250 × 18) for one month ` 250 for 17 months = ` (250 × 17) for one month ` 250 for 16 months = ` (250 × 16) for one month ` 250 for 15 months = ` (250 × 15) for one month ` 250 for 14 months = ` (250 × 14) for one month ` 250 for 13 months = ` (250 × 13) for one month ` 250 for 12 months = ` (250 × 12) for one month ` 250 for 11 month = ` (250 × 11) for one monthTherefore, for the whole deposit, we have:Equivalent principal for one month = ` 250 × (12 + 11 + 10 + … + 1)

= ` 250 × +12(12 1)2

(Using formula (i))

= ` (250 × 6 × 13) = ` 19500.


2.1.3 calculation of maturity amount on recurring depositThe interest on the recurring deposit account can be calculated by using the formula :

I = P × n(n 1) r2 12 100

+×

×

where I is the (simple) interest, P is the money deposited per month, n is the number of months for which the money has been deposited and r is the (simple) interest rate percent per annum.

The maturity value on a recurring deposit account can be calculated by using the formula:

MV = P × n + Iwhere MV is the maturity value, P is the money deposited per month, n is the number of months for which the money has been deposited and I is the (simple) interest.

NoteAll calculations are based on simple interest.

Calculation of (simple) interest and the maturity value (or amount) on a recurring (cumulative) deposit is illustrated with the help of following examples:


Example 1. Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate of 6% per annum and the monthly instalment is ` 1000, find the:

(i) interest earned in 2 years. (ii) matured value. (2015)

Solution. Here, P = money deposited per month = ` 1000.

n = number of months for which the money is deposited = 2 × 12 = 24 and

r = simple interest rate percent per annum = 6.

(i) Using the formula: I = P × + ××

( 1)2 12 100

n n r , we get

I (interest) = `24 252 12 100

1000 × 6 × × × = ` 1500.

(ii) Using the formula: MV = P × n + I, we get Matured value = ` (1000 × 24) + ` 1500 = ` 24000 + ` 1500 = ` 25500.

Example 2. Mohan deposits ` 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6% per annum.

(2006)

Solution. Here, P = money deposited per month = ` 80,

n = the number of months for which the money is deposited = 6 × 12 = 72 and r = interest rate percent per annum = 6.Using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

I = ` × × × ×

72 73 62 12 100

80 = ` 1051·20

Banking 23

Using the formula: MV = P × n + I, we get

maturity value = ` (80 × 72) + ` 1051·20

= ` 5760 + ` 1051·20 = ` 6811·20

Hence, the amount payable to Mohan on maturity = ` 6811·20

Example 3. Ahmed has a recurring deposit account in a bank. He deposits ̀ 2500 per month for 2 years. If he get ` 66250 at the time of maturity, find

(i) the interest paid by the bank. (ii) the rate of interest. (2011)

Solution. (i) Here, P = money deposited per month = ` 2500 and

n = the number of months for which the money is deposited = 2 × 12 = 24.

∴ Total money deposited by Ahmed = ` (2500 × 24) = ` 60000.

The money which Ahmed gets at the time of maturity = ` 66250.

∴ The interest paid by the bank = ` 66250 – ` 60000 = ` 6250.

(ii) Let the rate of interest be r% per annum, then by using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

` 6250 = ` 2500 × 24(24 1)2 12 100

r+×

× ⇒ 6250 = 25 × 25 × r ⇒ 6250 = 625 r ⇒ r = 10.

Hence, the rate of interest = 10% per annum.

Example 4. Shobana has a cumulative time deposit account in State Bank of India. She deposits ` 500 per month for a period of 4 years. If at the time of maturity she gets ` 28410, find the rate of (simple) interest.

Solution. Here, P = money deposited per month = ` 500 and n = the number of months for which the money is deposited = 4 × 12 = 48.Let the rate of interest be r% per annum, then by using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

I = ` 500 × 48 492 12 100

r××

× = ` 490 r.

Total money deposited by Shobana = ` (500 × 48) = ` 24000.∴ The amount of maturity = total money deposited + interest = ` 24000 + ` 490 r = ` (24000 + 490 r).According to given, 24000 + 490 r = 28410⇒ 490 r = 4410 ⇒ r = 9.Hence, rate of (simple) interest = 9% p.a.

Example 5. Richard has a recurring deposit account in a post office for 3 years at 7·5% p.a. simple interest. If he gets ` 8325 as interest at the time of maturity, find

(i) the monthly instalment (ii) the amount of maturity. (2017)


Solution. Here, n = the number of months for which the money is deposited = 3 × 12 = 36 and r = interest rate percent per annum = 7·5

(i) Let the monthly instalment be ` x, then P = ` x.

Using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

I = ` x × .36 37 7 5

2 12 100×

××

= ` 3 37 15 333

2 200 80x x×

× × = ` .


x = 8325 ⇒ x = 25 × 80 = 2000.

Hence, the monthly instalment = ` 2000. (ii) Total amount deposited by Richard = ` (2000 × 36) = ` 72000. ∴ Amount of maturity = total amount deposited + interest = ` 72000 + ` 8325 = ` 80325.

Example 6. Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is 8% per annum and Mr. Britto gets ` 8088 from the bank after 3 years, find the value of his monthly instalment. (2013)

Solution. Here, n = the number of months for which the money is deposited = 3 × 12 = 36 and r = interest rate percent per annum = 8.Let the monthly instalment be ` x, then P = ` x.Using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

I = ` x × 36 37 82 12 100×

××

= ` 11125 x.

Total money deposited by Mr. Britto = ` (x × 36) = ` 36x.∴ The amount of maturity = total money deposited + interest

= ` 36x + ` 11125

x = ` 101125

x.

But the amount of maturity = ` 8088 (given)

⇒ 101125

x = 8088 ⇒ 25x = 8 ⇒ x = 200.

Hence, the monthly instalment = ` 200.

Example 7. Priyanka has a recurring deposit account of `1000 per month at 10% per annum. If she gets ` 5550 as interest at the time of maturity, find the total time for which the account was held. (2018)

Solution. Here, P = money deposited per month = ` 1000 and

r = rate of interest per annum = 10.

Let the account be held for n months, then by using the formula:

I = P × n n r( )+×

×12 12 100

, we get

I = ̀ 1000 × n n( )+×

×12 12

10100

= ` 100 × n n( )+

×1

2 12 .

Banking 25

According to given, 100 × n n( )+ 1

24 = 5550

⇒ n (n + 1) = 24 5550

100×

⇒ n (n + 1) = 12 × 111

⇒ n2 + n – 1332 = 0 ⇒ (n – 36) (n + 37) = 0

⇒ n = 36, – 37 but n cannot be negative

⇒ n = 36.

Hence, the account was held for 36 months i.e. 3 years.

Example 8. Beena has a cumulative deposit account of ` 400 per month at 10% per annum simple interest. If she gets ` 30100 at the time of maturity, find the total time for which the account was held. (2018)

Solution. Here, P = money deposited per month = ` 400 and r = interest rate percent per annum = 10.Let the account be held for n months, then by using the formula:

I = P × ( 1)2 12 100

n n r+×

×, we get

I = ` 400 × ( 1) 102 12 100

n n +×

× = `

5 ( 1)3

n n + .

Total money deposited by Beena = ` (400 × n) = ` 400 n.∴ The amount of maturity = total money deposited + interest

= ` 400 n + ` 5 ( 1)

3n n +

= ` 1200 5 ( 1)

3n n n+ + = `

25 12053

n n+ .

According to given, 25 1205

3n n+ = 30100

⇒ 5n2 + 1205 n – 90300 = 0 ⇒ n2 + 241 n – 18060 = 0

⇒ (n – 60)(n + 301) = 0

⇒ n = 60, – 301 but n cannot be negative

⇒ n = 60.

Hence, the account was held for 60 months i.e. 5 years.

Exercise 2

1. Mrs. Goswami deposits ` 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value. (2009)

2. Sonia had a recurring deposit account in a bank and deposited `600 per month for

2 12

years. If the rate of interest was 10% p.a., find the maturity value of this account. (2018)

3. Kiran deposited ` 200 per month for 36 months in a bank’s recurring deposit account. If the banks pays interest at the rate of 11% per annum, find the amount she gets on maturity? (2012)

4. Haneef has a cumulative bank account and deposits ` 600 per month for a period of 4 years. If he gets ` 5880 as interest at the time of maturity, find the rate of interest.


5. David opened a Recurring Deposit Account in a bank and deposited ` 300 per month for two years. If he received ` 7725 at the time of maturity, find the rate of interest per annum. (2008)

6. Mr. Gupta opened a recurring deposit account in a bank. He deposited ` 2500 per month for two years. At the time of maturity he got ` 67500. Find :

(i) the total interest earned by Mr. Gupta. (ii) the rate of interest per annum. (2010)7. Shahrukh opened a Recurring Deposit Account in a bank and deposited ` 800 per month

for 1 12

years. If he received ` 15084 at the time of maturity, find the rate of interest per

annum. (2014)8. Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per

annum and Rekha receives ` 441 as interest at the time of maturity. Find the amount Rekha deposited each month. (2019)

9. Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets ` 1200 as interest at the time of maturity, find:

(i) the monthly instalment (ii) the amount of maturity. (2016)10. Mr. R.K. Nair gets ` 6455 at the end of one year at the rate of 14% per annum in a

recurring deposit account. Find the monthly instalment. (2005)11. Samita has a recurring deposit account in a bank of ` 2000 per month at the rate of 10%

p.a. If she gets ` 83100 at the time of maturity, find the total time for which the account was held.

Multiple Choice QuestionsChoose the correct answer from the given four options (1 to 3):

1. If Sharukh opened a recurring deposit account in a bank and deposited ` 800 per month

for 1 12

years, then the total money deposited in the account is

(a) ` 11400 (b) ` 14400 (c) ` 13680 (d) none of these2. Mrs. Asha Mehta deposit ` 250 per month for one year in a bank’s recurring deposit

account. If the rate of (simple) interest is 8% per annum, then the interest earned by her on this account is

(a) ` 65 (b) ` 120 (c) ` 130 (d) ` 2603. Mr. Sharma deposited ` 500 every month in a cumulative deposit account for 2 years.

If the bank pays interest at the rate of 7% per annum, then the amount he gets on maturity is

(a) ` 875 (b) ` 6875 (c) ` 10875 (d) ` 12875

Summary Recurring (or cumulative) deposit account Recurring (or cumulative) deposit account is a time deposit scheme in banks (or post

offices) to boost the savings among the people of small and middle income groups. Under this scheme, an investor deposits a fixed amount (in multiples of ` 5) every month for a specified number of months (usually, in multiples of 3) and on the expiry of this period (called maturity period), he/she gets the amount deposited by him/her together with the interest due to him/her. The amount received by the investor on the expiry of the specified period is called maturity value.

The rate of interest is revised from time to time.

Banking 27

Calculation of interest on a recurring deposit account The interest on a recurring deposit account can be calculated by using the formula:

I = P × ( 1)2 12 100

n n r+×

×

where I is the (simple) interest earned, P is the money deposited every month, n is the number of months for which the money has been deposited and r is the (simple) interest rate percent per annum.

Calculation of maturity amount on a recurring deposit account The maturity value (or amount) on a recurring deposit account can be calculated by

using the formula:MV = P × n + I

where MV is the maturity value, P is the money deposited every month, n is the number of months for which the money has been deposited and I is the (simple) interest earned on the recurring deposit account.

Chapter Test

1. Mr. Dhruv deposits ` 600 per month in a recurring deposit account for 5 years at the rate of 10% per annum (simple interest). Find the amount he will receive at the time of maturity.

2. Ankita started paying ` 400 per month in a 3 year recurring deposit. After six months

her brother Anshul started paying ` 500 per month in a 212

years recurring deposit. The

bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?

3. Shilpa has a 4 year recurring deposit account in Bank of Maharashtra and deposits ` 800 per month. If she gets ` 48200 at the time of maturity, find

(i) the rate of (simple) interest. (ii) the total interest earned by Shilpa.

4. Mr. Chaturvedi has a recurring deposit account in Grindlay’s Bank for 4 12

years at 11%

p.a. (simple interest). If he gets ` 101418·75 at the time of maturity, find the monthly instalment.

5. Rajiv Bhardwaj has a recurring deposit account in a bank of ` 600 per month. If the bank pays simple interest of 7% p.a. and he gets ` 15450 as maturity amount, find the total time for which the account was held.


3.1 shareTo start any big business (company or industry), a large sum of money is needed and, in general, it is not possible for an individual to invest such a large amount. Then some persons, interested in the business, join together and form a company. They divide the estimated money required into small parts. Each such part is called a share. A share may have value ` 5, ` 10, ` 25, ` 50, ` 100 etc. Each person who purchases one or more shares is called a shareholder.

3.1.1 some terms related with a share1. The original value of a share is called its nominal value (abbreviated N.V.) or face value

or printed value. The nominal value of a share always remains same.2. The price of a share at any time is called its market value (abbreviated M.V.) or cash

value. The market value of a share changes from time to time.3. If the market value of a share is the same as its nominal value, the share is called at

par.4. If the market value of a share is more than its nominal value, the share is called at

premium or above par. If a share of ` 100 is selling at ` 135, then it is said to be selling at a premium of ` 35 or at ` 35 above par.

5. If the market value of a share is less than its nominal value, the share is called at discount or below par. If a share of ` 100 is selling at ` 88, then it is said to be selling at a discount of ` 12 or at ` 12 below par.

3.2 dividendThe profit, which a shareholder gets for his/her investment from the company, is called dividend.1. The dividend is always expressed as the percentage of the face value of the share.2. The dividend is always given (by the company) on the face value of the share irrespective

of the market value of the share.

3.2.1 Quotations“15% ` 100 shares at ` 145” means that(1) the face value of 1 share = ` 100.(2) the market value of 1 share = ` 145.(3) the dividend (profit) on 1 share = 15% of ` 100 = ` 15 p.a.(4) the income on ` 145 is ` 15 for one year.

(5) the rate of return (or yield) p.a. = 15145

100 × % = 300

29% = 10 10

29%.

3 Shares and Dividends

Shares and Dividends 29

Similarly, “12% ` 25 shares at a discount of ` 5” means that(1) the face value of 1 share = ` 25.(2) the market value of 1 share = ` 25 – ` 5 = ` 20.

(3) the dividend on 1 share = 12% of ` 25 = ` 12

10025 ×

p.a. = ` 3 p.a.(4) the income on ` 20 is ` 3.

(5) the rate of return p.a. = 320

100 × % = 15%.

3.3 Formulae1. Investment Money invested = number of shares × market value of one share.2. Income and Return (i) Annual income = number of shares × rate of dividend × face value of one share

(ii) Rate of return = annual income

investment×

100 %

3. Number of shares

Number of shares purchased (or held) = investment annual incomemarket value of one share income on one share

or .


Example 1. A man purchases 600 shares of face value ` 40 at par. If a dividend of ` 1680 was received at the end of the year, find the rate of dividend.

Solution. Total value of all the shares (investment) = ` (40 × 600) = ` 24000.The dividend received at the end of year = ` 1680.

∴ The rate of dividend = 168024000

100 × % = 7%.

Example 2. Raman has 450 shares of ` 200 of a company paying a dividend of 16%. Find his net income after paying an income tax of 20%.

Solution. Total dividend = number of shares × rate of dividend × face value of one share

= 450 × 16100

× ` 200 = ` 14400.

Income tax = 20% of ` 14400 = ` 20100

14400 × = ` 2880.∴ Net income = total dividend – income tax = ` 14400 – ` 2880 = ` 11520.

Example 3. A man bought 500 shares, each of face value ` 10, of a certain business concern and during the first year after purchase received ` 400 as dividend on his shares. Find the rate of dividend on shares.

Solution. Let the rate of dividend be r % per annum.Annual dividend = number of shares × rate of dividend × face value of one share

= 500 × 100

r × ` 10 = ` 50 r

Given, dividend received after one year of purchase of shares is ` 400.∴ ` 50 r = ` 400 ⇒ 50 r = 400 ⇒ r = 8.Hence, the rate of dividend = 8%.


Example 4. A man invests ` 9600 on ` 100 shares at ` 80. If the company pays him 18% dividend, find :

(i) the number of shares he buys. (ii) his total dividend. (iii) his percentage return on the shares. (2012)

Solution. (i) Investment = ` 9600, market value of one share = ` 80.

∴ The number of shares bought = investmentmarket value of one share

= 960080

``

= 120.

(ii) Total dividend = number of shares × rate of dividend × face value of one share

= 120 × 18100

× ` 100 = ` 2160.

(iii) ` 2160 is the income on ` 9600,

∴ rate of return on shares = 21609600

100 × % = 45

2% = 22·5%.

Example 5. A man invests ` 3960 in shares of a company which pays 15% dividend at a time when a ` 25 share costs ` 33. Find :

(i) the number of shares he bought. (ii) the annual income from his shares. (iii) the rate of interest which he gets on his investment.

Solution. (i) Since the market value of one share is ` 33 and the money invested is ` 3960,

∴ the number of shares bought = 396033

``

= 120.

(ii) Annual income = number of shares × rate of dividend × face value of one share

= 120 × 15100

× ` 25 = ` 450.

(iii) ` 450 can be considered as the interest on ` 3960 for one year,

∴ the rate of interest = 4503960

100 × % = 125

11% = 11 4

11%.

Example 6. A man wants to buy 62 shares available at ` 132 (par value of ` 100). (i) How much should he invest ? (ii) If the dividend is 7·5%, what will be his annual income ? (iii) If he wants to increase his annual income by ` 150, how many extra shares should

he buy ? (2002)Solution. (i) Since the market value of one share (par value ` 100) is ` 132,∴ market value of 62 shares = ` (132 × 62) = ` 8184.∴ The man should invest ` 8184.(ii) Annual income = number of shares × rate of dividend × face value of one share

= 62 × .7 5

100 × ` 100

= ` (62 × 7·5) = ` 465.(iii) Since income on one share is ` 7·5,

∴ for income of ` 150, the number of shares = 150.7 5

``

= 20.

Thus, to increase the income by ` 150, the number of extra shares to be purchased = 20.


Example 7. A man invests ` 22500 in ` 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:

(i) the number of shares purchased. (ii) the annual dividend received. (iii) the rate of return he gets on his investment. Give your answer correct to the

whole number. (2018)

Solution. (i) Since the man invests in ` 50 shares available at 10% discount, the market value of one share

= 1 10100

−

of `50 = ` 50 910

×

= `45.

As the investment is ` 22500,

∴ the number of shares purchased = `

`

2250045 = 500.

(ii) Annual dividend received = number of shares × rate of dividend × face value of one share

= 500 × 12

100 × ` 50

= ` (5 × 12 × 50) = ` 3000.

(iii) `3000 can be considered as income on `22500,

∴ rate of return = 300022500

100×

% =

403

13

13% %=

Hence, the rate of return on his investment = 13% (nearest to the whole number).

Example 8. Mr. Parekh invested ` 52000 on ` 100 shares at a discount of ` 20 paying 8% dividend. At the end of one year he sells the shares at a premium of ` 20. Find

(i) the annual dividend (ii) the profit earned including his dividend. (2011)

Solution. Market value of one share = ` 100 – ` 20 = ` 80, investment = ` 52000.

∴ The number of shares bought = 5200080

``

= 650.

(i) The annual dividend = number of shares × rate of dividend× face value of one share

= 650 × 8100

× ` 100 = ` 5200.

(ii) As Mr. Parekh sells his shares at a premium of ` 20, the market value of one share = ` 100 + ` 20 = ` 120.∴ The selling value of his 650 shares = ` (120 × 650) = ` 78000.∴ Profit earned including his dividend = selling value + dividend – investment = ` 78000 + ` 5200 – ` 52000 = ` 31200.

Example 9. How much should a man invest in ` 50 shares selling at ` 60 to obtain an income of ` 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number. (2017)


Solution. Dividend on one share of ` 50 = 10% of ` 50

= ` 10100

50 × = ` 5.

Since the total income is ` 450,

∴ the number of shares bought = annual incomeincome on one share

= 4505

``

= 90.

Since the market value of one share = ` 60,∴ the investment = number of shares × market value of one share = ` (60 × 90) = ` 5400.

Yield percent i.e. rate of return = annual incomeinvestment

100 × %

= 4505400

100 ×

``

% = 45054

%

= 253

% = 8 13

%

= 8% , nearest to the whole number.

Example 10. Salman invests a sum of money in ` 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is ` 600, calculate:

(i) the number of shares he bought. (ii) his total investment. (iii) the rate of return on his investment. (2014)

Solution. (i) Dividend on one share = 15% of ` 50

= ` 15100

50 × = ` 15

2.

Since Salman’s annual dividend is ` 600,

∴ the number of shares bought by Salman = annual incomedividend on one share

= 600152

`

` = 600 × 2

15 = 80.

(ii) As Salman bought shares of ` 50 at 20% premium, market value of one share

= ` 20100

1

+ × 50 = ` 65

50 × = ` 60.

∴ His total investment = number of shares × market value of one share = ` (80 × 60) = ` 4800.

(iii) Rate of return = annual incomeinvestment

100 × %

= 6004800

100

× ``

% = 252

% = 12∙5%

Example 11. A man sold 400 (` 20) shares paying 5% at ` 18 and invested the proceeds in (` 10) shares, paying 7% at ` 12. How many (` 10) shares did he buy and what was the change in income?

Solution. Selling price of 400 (` 20) shares at ` 18 = ` (18 × 400) = ` 7200.


Market price of ` 10 share = ` 12,

∴ the number of ` 10 shares purchased = 720012

``

= 600.

Annual income from original (` 20) shares = number of shares × rate of dividend × face value of one share

= 400 × 5100

× ` 20 = ` 400.

Annual income from new (` 10) shares = number of shares × rate of dividend × face value of one share

= 600 × 7100

× ` 10 = ` 420.

∴ Change in annual income = ` 420 – ` 400 = ` 20 (increase).

Example 12. Vivek invests ` 4500 in 8%, ` 10 shares at ` 15. He sells the shares when the price rises to ` 30, and invests the proceeds in 12% ` 100 shares at ` 125. Calculate

(i) the sale proceeds. (ii) the number of ` 125 shares he buys. (iii) the change in his annual income from dividend. (2010)

Solution. Market value of ` 10 share is ` 15, investment = ` 4500.

∴ The number of shares purchased by Vivek = investmentmarket value of one share

= 450015

``

= 300. (i) Selling price of one share = ` 30. ∴ Selling price of 300 shares = ` (30 × 300) = ` 9000. Hence, Vivek’s sale proceeds = ` 9000. (ii) He invests his proceeds in 12% ` 100 shares at ` 125. Investment = ` 9000, market value of one share = ` 125.

∴ The number of new shares bought = 9000125

``

= 72.

(iii) Annual income (dividend) from previous shares = number of shares × rate of dividend × face value of one shares

= 300 × 8100

× ` 10 = ` 240.

Annual income (dividend) from new shares = number of shares × rate of dividend × face value of one share

= 72 × 12100

× ` 100 = ` 864.

∴ Change in income = ` 864 – ` 240 = ` 624 (increase).

Example 13. Rohit invested ` 9600 on ` 100 shares at ` 20 premium paying 8% dividend. Rohit sold the shares when the price rose to ` 160. He invested the proceeds (excluding dividend) in 10% ` 50 shares at ` 40. Find the :

(i) original number of shares. (ii) sale proceeds. (iii) new number of shares. (iv) change in the two dividends. (2015)

Solution. (i) Rohit invested ` 9600 on ` 100 shares at 20% premium paying 8% dividend.

Market value of one share = ` 20100

1

+ × 100 = ` 120.


∴ The original number of shares purchased = investmentmarket value of one share

= 9600120

``

= 80.

(ii) Selling price of one share = ` 160, ∴ selling price of 80 shares = ` (160 × 80) = ` 12800. Hence, Rohit’s sale proceeds = ` 12800. (iii) Market value of new share = ` 40, investment = ` 12800.

∴ The number of new shares purchased = investmentmarket value of one share

= 1280040

``

= 320.

(iv) Annual income (dividend) from original shares = number of shares × rate of dividend × face value of one

share

= 80 × 8100

× ` 100 = ` 640.

Annual income (dividend) from new shares = number of shares × rate of dividend × face value of one share

= 320 × 10100

× ` 50 = ` 1600

∴ Change in two dividends = ` 1600 – ` 640 = ` 960 (increase)

Example 14. Which is better investment : 7% ` 100 shares at ` 120 or 8% ` 10 shares at ` 13·50?

Solution. In the first case : Income on ` 120 = 7% of ` 100 = ` 7,

∴ income on ` 1 = ` 7

120.

In the second case : Income on ` 13·50 = 8% of ` 10 = `

810

,

∴ income on ` 1 = ̀

810.13 50

= `

8 210 27

× = `

8135

.

Now 7 7 9 63120 120 9 1080

×= =

× and 8 8 8 64

135 135 8 1080×

= =×

.

Since 63 < 64, therefore, the investment in the second case is better than the investment in the first case.

Example 15. By purchasing ` 25 gas shares for ` 10 each, a man gets 4 percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?

Solution. Since the man gets 4% profit on his investment,∴ income on 1 share of market value ` 10 = 4% of ` 10

= ` 4

10010 ×

= ` 4

10.

Since the nominal value of 1 share is ` 25,

∴ on ` 25, company pays = ` 4

10

∴ on ` 100, company pays = ` 4 100

10 25 ×

= ` 1·6

∴ Rate percent which the company pays = 1·6 %


Income on one share = ` 4

10.

∴ Income on 60 shares = ` ×

410

60 = ` 24.

Example 16. Mr. Lohia invests ` 26680 in buying ` 50 shares at a discount of 8%. He sells shares worth ` 15000 at a premium of 6% and the rest at a discount of 10%. Find his total gain or loss from the transaction.

Solution. As Mr. Lohia buys shares at a discount of 8%,

market value of one share = 8100

1

− of ` 50 = ` 46.

∴ The number of shares purchased = 2668046

``

= 580.

Number of shares worth (face value) ` 15000 = 1500050

``

= 300.

He sold 300 shares at a premium of 6%,


1

+ of ` 50 = ` 53.

∴ The selling value of 300 shares at ` 53 each = ` (300 × 53) = ` 15900. The number of remaining shares = 580 – 300 = 280. Lohia sold 280 shares at discount of 10%,


1

− of ` 50 = ` 45.

∴ The selling value of 280 shares at ` 45 each = ` (280 × 45) = ` 12600.∴ Total selling value = ` 15900 + ` 12600 = ` 28500.∴ Lohia’s total gain = ` 28500 – ` 26680 = ` 1820.

Example 17. Mr. Ram Gopal invested ` 8000 in 7% ` 100 shares at ` 80. After a year he sold these shares at ` 75 each and invested the proceeds (including his dividend) in 18% ` 25 shares at ` 41. Find:

(i) his dividend for the first year. (ii) his annual income in the second year. (iii) the percentage increase in his return on his original investment. (2006)

Solution. (i) Since Mr. Ram Gopal invested ` 8000 at ` 80 per share,

the number of shares bought by him = 800080

``

= 100.

Dividend received on one share = 7% of ` 100 = ` 7. ∴ The total dividend received after a year = ` (7 × 100) = ` 700. ∴ His dividend for the first year = ` 700. (ii) As Mr. Ram Gopal sold his shares at ` 75 each, the sale value of his shares = ` (75 × 100) = ` 7500.


His investment in new shares i.e. his proceeds = dividend received + sale value of shares = ` 700 + ` 7500 = ` 8200. As Mr. Ram Gopal invested his proceeds i.e. ` 8200 in ` 25 shares at ` 41 each,

the number of new shares purchased = 820041

``

= 200.

Dividend received on one share = 18% of ` 25

= ` 18100

25 × = `

92 .

∴ Total dividend received on his second investment = ` 92

200 × = ` 900.

∴ His annual income in the second year = ` 900. (iii) The increase in return = dividend on second investment – dividend on first investment = ` 900 – ` 700 = ` 200. ∴ The percentage of increase in return on his original investment

= 2008000

100 × % = 5

2% = 2·5%.

Example 18. Amit and Richa invest ` 12000 each in buying shares of two companies. Amit buys 15% ` 100 shares at a discount of ` 20, while Richa buys ` 25 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Richa’s company.

Solution. Market value of one share purchased by Amit = ` 100 – ` 20 = ` 80. Investment by Amit = ` 12000.

∴ Number of shares purchase by Amit = 1200080

``

= 150.

Annual dividend received by Amit = number of shares held by Amit × rate of dividend × face value of one share held by Amit

= 150 × 15100

× ` 100 = ` 2250.

∴ Annual dividend received by Richa = ` 2250.(Q Both Amit and Richa get equal dividends)

Richa purchased ` 25 shares at premium of 20%.

∴ Market value of one share purchased by Richa = 20100

1

+ of ` 25

= ` × 6

525 = ` 30.

Investment by Richa = ` 12000.

∴ Number of shares purchased by Richa = 1200030

``

= 400.

Let r% be the rate of dividend declared by Richa’s company, then

annual dividend of Richa = number of shares held by Richa × rate of dividend of Richa’s company × face value of one share held by Richa


⇒ ` 2250 = 400 × 100

r × ` 25

⇒ 2250 = 100r ⇒ r = 22·5Hence, the rate percent of the dividend declared by Richa’s company = 22·5%

Example 19. A dividend of 9% was declared on ` 100 shares selling at a certain price. If

the rate of return is 7 12

%, calculate : (i) the market value of the share. (ii) the amount to be invested to obtain an annual dividend of ` 630. (2000)

Solution. Dividend on one share of ` 100 = ` 9.(i) Let the market value of one share be ` x.

The profit on one share = 7 12

% of ` x = ` 15 12 100

x × × = ` 3

40x .

Since the dividend paid on one share = ` 9,

∴ 340

x = 9 ⇒ x = 120.

∴ The market value of each share = ` 120.(ii) As the total income is ` 630,

∴ the number of shares bought = 6309

``

= 70.

Since the market value of each share = ` 120,∴ the amount to be invested = ` (120 × 70) = ` 8400.

Example 20. A man buys ` 50 shares of a company which pays 12% dividend. He buys the shares at such a price that his profit is 15% on his investment. At what price did he buy the shares?

Solution. Dividend on 1 share of ` 50 = 12% of ` 50 = ` 6.Let the man buy one share for ` x.

His profit on one share = 15% of ` x = ` 15

100x.

Since the dividend paid by the company on 1 share = ` 6,

∴ 15100

x = 6 ⇒ x = 40.

∴ The man buys each share at ` 40.

Example 21. Suresh has a choice to invest in shares of two companies A and B. ` 100 shares of company A are available at 10% premium and it pays 8% dividend whereas ` 50 shares of company B are available at 12% discount and it pays 7% dividend. If he invests equally in both the companies and the sum of his annual incomes from them is ` 1340, find how much, in all, does he invest?

Solution. Let Suresh invest ` x in each company.For company A Face value of each share = ` 100,

market value of each share = 10100

1

+ of ` 100 = ` 110.

∴ The number of shares bought = 110 110

x x=

``

.


Annual income = no. of shares × rate of dividend × F.V. of one share

= 8110 100

x× × ` 100 = `

455

x .

For company B Face value of each share = ` 50,

market value of each share = 12100

1

− of ` 50 = ` 44.

∴ The number of shares bought = 44 44x x

=``

.

Annual income = no. of shares × rate of dividend × F.V. of one share

= 744 100x

× × ` 50 = ` 788

x .

∴ Sum of annual income from both companies = ` 455

x + ` 788

x

= ` 4 755 88

x x + = `

4 75 8

+ ×

11x

= ` 32 35

40 11x+

× = ` 67440

x .

According to given, ` 67440

x = ` 1340 ⇒ 67440

x = 1340 ⇒ x = 8800

⇒ Suresh invests ` 8800 in each company.∴ Suresh invests in all = ` 8800 + ` 8800 = ` 17600.

Example 22. A man invests ` 13500 partly in 6% ` 100 shares at ` 140 and partly in 5% ` 100 shares at ` 125. If his total income is ` 560, how much has he invested in each?

Solution. Let the investment of the man in 6% ` 100 shares at ` 140 be ` x, then his investment in 5% ` 100 shares at ` 125 = ` (13500 – x). Income on one share of ` 140 = ` 6% of ` 100 = ` 6.

∴ Income on ` x = ` 6

140x = `

370

x.

Income on one share of ` 125 = ` 5% of ` 100 = ` 5.

∴ Income on ` (13500 – x) = ` 5

125 (13500 – x)

= ` 125

(13500 – x).

But the total income of the man is ` 560,

∴ 370

x + 125

(13500 – x) = 560

⇒ 15x + 14 (13500 – x) = 350 × 560⇒ 15x – 14x = 350 × 560 – 14 × 13500⇒ x = 7000.∴ 13500 – x = 13500 – 7000 = 6500.∴ Investment in 6% shares at ` 140 = ` 7000and investment in 5% shares at ` 125 = ` 6500.


Exercise 3

1. Find the dividend received on 60 shares of ` 20 each if 9% dividend is declared.

2. A company declares 8 percent dividend to the shareholders. If a man receives ` 2840 as his dividend, find the nominal value of his shares.

HintLet the nominal value of his shares be ` x, then 8% of ` x = ` 2840.

3. A man buys 200 ten-rupee shares at ` 12·50 each and receives a dividend of 8%. Find the amount invested by him and the dividend received by him in cash.

4. Find the market price of 5% ` 100 share when a person gets a dividend of ` 65 by investing ` 1430.

5. Salman buys 50 shares of face value ` 100 available at ` 132. (i) What is his investment? (ii) If the dividend is 7·5% p.a., what will be his annual income? (iii) If he wants to increase his annual income by ` 150, how many extra shares should

he buy? (2013)

6. A lady holds 1800, ` 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return does she get on her investment ?

7. What sum should a person invest in ` 25 shares, selling at ` 36, to obtain an income of ` 720, if the dividend declared is 12%? Also find the percentage return on his income.

8. Ashok invests ` 26400 on 12% ` 25 shares of a company. If he receives a dividend of ` 2475, find:

(i) the number of shares he bought. (ii) the market value of each share. (2016)

9. A man invests ` 4500 in shares of a company which is paying 7·5% dividend. If ` 100 shares are available at a discount of 10%, find

(i) the number of shares he purchases. (ii) his annual income. (2019)

10. Amit Kumar invests ` 36000 in buying ` 100 shares at ` 20 premium. The dividend is 15% per annum. Find :

(i) the number of shares he buys. (ii) his yearly dividend. (iii) the percentage return on his investment. (2009)

11. Mr. Tiwari invested ` 29040 in 15% ` 100 shares at a premium of 20%. Calculate : (i) the number of shares bought by Mr. Tiwari. (ii) Mr. Tiwari‘s income from the investment. (iii) the percentage return on his investment. (2005)

12. A man buys shares at the par value of ` 10 yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of ` 300.

13. A man invests ` 8800 on buying shares of face value of rupees hundred each at a premium of 10%. If he earns ` 1200 at the end of year as dividend, find :

(i) the number of shares he has in the company. (ii) the dividend percentage per share.


14. A man invested ` 45000 in 15% ` 100 shares quoted at ` 125. When the market value of these shares rose to ` 140, he sold some shares, just enough to raise ` 8400. Calculate:

(i) the number of shares he still holds. (ii) the dividend due to him on these shares. (2004)

15. Ajay owns 560 shares of a company. The face value of each share is ` 25. The company declares a dividend of 9%. Calculate:

(i) the dividend that Ajay will get. (ii) the rate of interest, on his investment, if Ajay has paid ` 30 for each share. (2007)

16. A company with 10000 shares of nominal value of ` 100 declares an annual dividend of 8% to the shareholders.

(i) Calculate the total amount of dividend paid by the company. (ii) Ramesh bought 90 shares of the company at ` 150 per share.

Calculate the dividend he received and the percentage return on his investment.

17. A company with 4000 shares of nominal value of ` 110 declares annual dividend of 15%. Calculate:

(i) the total amount of dividend paid by the company. (ii) the annual income of Shah Rukh who holds 88 shares in the company. (iii) if he received only 10% on his investment, find the price Shah Rukh paid for each

share. (2008)

18. By investing ` 7500 in a company paying 10 percent dividend, an income of ` 500 is received. What price is paid for each ` 100 share?

19. A man buys 400 ten-rupee shares at a premium of ` 2·50 on each share. If the rate of dividend is 8%, find

(i) his investment (ii) dividend received (iii) yield.

20. A man invests ` 10400 in 6% shares at ` 104 and ` 11440 in 10·4% shares at ` 143. How much income would he get in all?

21. Two companies have shares of 7% at ` 116 and 9% at ` 145 respectively. In which of the shares would the investment be more profitable?

22. Which is better investment : 6% ` 100 shares at ` 120 or 8% ` 10 shares at ` 15 ?

23. A man invests ` 10080 in 6% hundred-rupee shares at ` 112. Find his annual income. When the shares fall to ` 96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at ` 8. Find the change in his annual income.

24. Sachin invests ` 8500 in 10% ` 100 shares at ` 170. He sells the shares when the price of each share rises by ` 30. He invests the proceeds in 12% ` 100 shares at ` 125. Find

(i) the sale proceeds. (ii) the number of ` 125 shares he buys. (iii) the change in his annual income. (2019)

25. A person invests ` 4368 and buys certain hundred-rupee shares at ` 91. He sells out shares worth ` 2400 when they have risen to ` 95 and the remainder when they have fallen to ` 85. Find the gain or loss on the total transaction.

26. By purchasing ` 50 gas shares for ` 80 each, a man gets 4% profit on his investment. What rate percent is company paying? What is his dividend if he buys 200 shares?

27. ` 100 shares of a company are sold at a discount of ` 20. If the return on the investment is 15%, find the rate of dividend declared.

28. A company declared a dividend of 14%. Find the market value of ` 50 shares if the return on the investment was 10%.


29. A company with 10000 shares of ` 100 each, declares an annual dividend of 5%. (i) What is the total amount of dividend paid by the company? (ii) What would be the annual income of a man, who has 72 shares, in the company? (iii) If he received only 4% on his investment, find the price he paid for each share.

30. A man sold some ` 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in ` 100 shares paying 16% dividend quoted at ` 80 and thus increased his income by ` 2000. Find the number of shares sold by him.

31. A man invests ` 6750, partly in shares of 6% at ` 140 and partly in shares of 5% at ` 125. If his total income is ` 280, how much has he invested in each?

32. Divide ` 20304 into two parts such that if one part is invested in 9% ` 50 shares at 8% premium and the other part is invested in 8% ` 25 shares at 8% discount, then the annual incomes from both the investments are equal.

Multiple Choice QuestionsChoose the correct answer from the given four options (1 to 6):

1. If Jagbeer invests ` 10320 on ` 100 shares at a discount of ` 14, then the number of shares he buys is

(a) 110 (b) 120 (c) 130 (d) 150

2. If Nisha invests ` 19200 on ` 50 shares at a premium of 20%, then the number of shares she buys is

(a) 640 (b) 384 (c) 320 (d) 160

3. ` 40 shares of a company are selling at 25% premium. If Mr. Jacob wants to buy 280 shares of the company, then the investment required by him is

(a) ` 11200 (b) ` 14000 (c) ` 16800 (d) ` 8400

4. Arun possesses 600 shares of ` 25 of a company. If the company announces a dividend of 8%, then Arun’s annual income is

(a) ` 48 (b) ` 480 (c) ` 600 (d) ` 1200

5. A man invests ` 24000 on ` 60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is

(a) ` 3000 (b) ` 2880 (c) ` 1500 (d) ` 1440

6. Salman has some shares of ` 50 of a company paying 15% dividend. If his annual income is ` 3000, then the number of shares he possesses is

(a) 80 (b) 400 (c) 600 (d) 800

Summary A share is one part from a finite number of equal parts in the capital of a company. It is

a small unit in which the capital of the company is divided and sold to raise money. Shareholder. Each person who purchases one or more shares is called a shareholder. Some terms related with a share 1. The original value of a share is called its nominal value (abbreviated N.V.) or face

value or printed value. The nominal value of a share always remains same. 2. The price of a share at any time is called its market value (abbreviated M.V.) or cash

value. The market value of a share changes from time to time. 3. If the market value of a share is the same as its nominal value, the share is called at

par.


4. If the market value of a share is more than its nominal value, the share is called at premium or above par. If a share of ` 100 is selling at ` 135, then it is said to be selling at a premium of ` 35 or at ` 35 above par.

5. If the market value of a share is less than its nominal value, the share is called at discount or below par. If a share of ` 100 is selling at ` 88, then it is said to be selling at a discount of ` 12 or at ` 12 below par.

Dividend The profit, which a shareholder gets for his investment from the company, is called dividend. 1. The dividend is always expressed as the percentage of the face value of the share. 2. The dividend is always given (by the company) on the face value of the share

irrespective of the market value of the share. Quotations “15% ` 100 shares at ` 145” means that 1. the face value of 1 share = ` 100. 2. the market value of 1 share = ` 145. 3. the dividend (profit) on 1 share = 15% of ` 100 = ` 15 p.a. 4. the income on ` 145 is ` 15 for one year.

5. the rate of return (or yield) p.a. = 15145

30029

1029

100 10×

= =% % % .

Similarly, “12% ` 25 shares at a discount of ` 5” means that 1. the face value of 1 share = ` 25. 2. the market value of 1 share = ` 25 – ` 5 = ` 20.

3. the dividend on 1 share = 12% of ` 25 = `

12100

25×

p.a. = ` 3 p.a.

4. the income on ` 20 is ` 3.

5. the rate of return p.a. = 320

100×

% = 15%.

Formulae 1. Investment Money invested = number of shares × market value of one share. 2. Income and Return (i) Annual income = number of shares × rate of dividend × face value of one share.

(ii) Rate of return = annual income

investment100 × %.

3. Number of shares Number of shares purchased (or held)

= investment annual incomemarket value of one share income on one share

or .


Chapter Test

1. If a man received ` 1080 as dividend from 9% ` 20 shares, find the number of shares purchased by him.

2. Find the percentage interest on capital invested in 18% shares when a ` 10 share costs ` 12.

Hint Dividend on one share = 18% of ` 10 = `

18100

10 × = `

95

.

Rate of return = income on one sharemarket value of one share

100 × %

=

99 15

12 5 12100 % 100 %

× = × ×

`

` = 15%.

3. Rohit Kulkarni invests ` 10000 in 10% ` 100 shares of a company. If his annual dividend is ` 800, find :

(i) the market value of each share. (ii) the rate percent which he earns on his investment.

4. At what price should a 9% ` 100 share be quoted when the money is worth 6% ?

5. By selling at ` 92, some 2·5% ` 100 shares and investing the proceeds in 5% ` 100 shares at ` 115, a person increased his annual income by ` 90. Find :

(i) the number of shares sold. (ii) the number of shares purchased. (iii) the new income. (iv) the rate percent which he earns on his investment.

6. A man has some shares of ` 100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% ` 50 shares at a premium of ` 10. This transaction decreases his income from dividends by ` 120. Calculate :

(i) the number of shares before the transaction. (ii) the number of shares he sold. (iii) his initial annual income from shares.

7. Divide ` 101520 into two parts such that if one part is invested in 8% ` 100 shares at 8% discount and the other in 9% ` 50 shares at 8% premium, the annual incomes are equal.

8. A man buys ` 40 shares of a company which pays 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share?

9. A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be ` 4675, find his savings and the amount which he invested in buying shares of each company.

10. Virat and Dhoni invest ` 36000 each in buying shares of two companies. Virat buys 15% ` 40 shares at a discount of 20%, while Dhoni buys ` 75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni’s company.

Documents

understAnding icse MAtheMAticsjesusandmary.in/notices/ICSE Maths 10 Sec-1 Chps 1-3.pdf · 2020. 4. 23. · ICSE examinations. The subject matter contained in this book has been explained