Business Mathematics 3 Nov

www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

BUSINESS MATHEMATICS

AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –

World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship

OPEN FOR ALL FREE FOR ALL


BUSINESS MATHEMATICS

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: 9414430763

[email protected]

www.afterschool.tk, www.afterschoool.tk


• The number of squares which we can form on a chessboard is

• (a) 64 (b) 160 (c) 224 (d) 204

• SOLUTION:

• 204


IN HOW MANY WAYS CAN WE ARRANGE 21 WHITE BALLS AND

3 BLACK BALLS IN A ROW SO THAT NO TWO BLACK BALLS

ARE PLACED TOGETHER

• There are 22 spots for you to put black balls. (one each between two white balls =20 and one before and one after these).

• 22C 3 = (22*21*20) / (6) =1540 answer


A 7 member committee is to be formed out of 8 boys & 5 girls. What is the probability that the

committee will have at least 2 girls?

• Total number of possibilities:

• 13C 7 = (13*12*11*10*9*8)/(6*5*4*3*2)

• =1716

• Favourable possibilities:

• 2 girls + 5 boys: (8c5 *5c2) =56*10


Continued . . .

• Favourable possibilities:

• 4 boys+ 3 girls =: (8c4 *5c3) =70*10

• 3 boys+ 4 girls =: (8c3 *5c4) =56*5

• 2 boys+ 5 girls =: (8c2 *5c5) =28*1

• =560+700+280+28 =1568

• Thus required probability is 1568 / 1716

• Answer.


Goti has some friends, out of whom, he can invite 4 persons in

exactly 70 numbers of ways (that is the maximum possible options that he can have in all his friends). Ram has just one less number of friends,

he has half the total options that Goti has for inviting maximum number of friends. How many

friends does Ram has? .


Solution

• Maximum number of options are available on mid point. Thus Goti has 8 friends.

• 8C4 = 70

• 7C4 = 35

• Thus Ram has 7 friends. Answer.


There are 15 seats (from 1 to 15). Seat no. 6 is already occupied. In

how many ways can be give 3 seats out of these seats to people

in such a way that no two consecutive seats are occupied?


Solution

• We have seats as under: • 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,• Seat no. 5,6,7 cannot be used, Now we have

12 seats left. There are following possiblities: • 2 persons before 5 and 1 person after 7 =24• 1 person before 5 and 2 persons after 7=84• 3 persons after 7 = 20• Total = 128 answer.


Solution:

• 2 persons before 5 and 1 person after 7 =24 = =3*8 = 24 alternatively 3c2 *8C1 = 24

• 1 person before 5 and 2 persons after 7=84 = (4c1 * 7c2) = 4*21 = 84

• 3 persons after 7 = (8-3+1) C3 = 20

• Add them together = 128 answer.


A retailer buys a sewing machine at a discount of 15% and sells it for

Rs. 1955. Thus, he makes a profit of 15%. The discount is:

(a) Rs. 270 (b) Rs. 290 (c) Rs. 300(d) Rs. 280


Solution …

• Sale price = 1955

• Cost price = 1955*100/115 = 1700

• Discount amount =

• 1700*15/85 = 300 answer.


The marked price of an article is 10% higher than the cost price. A dis of 10% is given on the marked price. In this kind of sale, the seller

• (a) bears no loss, no gain (c) loses 1%

• (b) gains 1% (d) None of these


Solution

• 1% loss always in such cases

• Suppose the cost is 100, marked price is 110. Discount is 11. Net loss is Re. 1 .


Solve it

• On an article with marked price Rs. 20000, a customer has a choice between three successive discounts of 20%, 20% and 10% and three successive discounts of 40% 5% and 5% By choosing the better offer he can save:

• (a) nothing (b) Rs. 690 (c) Rs. 715(d) Rs. 785


Solution

• 1st option: =20000*.8*.8*.9 = 11520

• 2nd option: =20000*.6*.95*.95 =10830

• In the first option, he will pay 11520 and in 2nd option he will pay Rs. 10830.

• Thus he will gain Rs. 690 in the 2nd option.

• Answer.


ABOUT AFTERSCHO☺OL

Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.


Why such A programme?

• To promote people to take up entrepreneurship and help develop the society

• To enable people to take up franchising and other such options to startA business / social development project

• To enable people to take up social development as their mission

• To enable people to promote spirituality and positive thinking in the world


Who are our supporters?

• Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us.

• You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.


About AFTERSCHO☺OL PGPSE – the best programme for developing great

entrepreneurs• Most flexible, adaptive but rigorous programme• Available in distance learning mode• Case study focused- latest cases • Industry oriented practical curriculum• Designed to make you entrepreneurs – not just

an employee• Option to take up part time job – so earn while

you learn • The only absolutely free course on internet


Workshops from AFTERSCHO☺OL

• IIF, Delhi• CIPS, Jaipur• ICSI Hyderabad Branch• Gyan Vihar, Jaipur• Apex Institute of Management, Jaipur• Aravali Institute of Management, Jodhpur• Xavier Institute of Management, Bhubaneshwar • Pacific Institute, Udaipur• Engineering College, Hyderabad


Flexible Specialisations:

• Spiritualising business and society• Rural development and transformation• HRD and Education, Social Development• NGO and voluntary work• Investment analysis,microfinance and inclusion • Retail sector, BPO, KPO• Accounting & Information system (with CA / CS /CMA)• Hospital management and Health care• Hospitality sector and culture and heritage• Other sectors of high growth, high technology and social

relevance


Salient features:• The only programme of its kind (in the whole world)• No publicity and low profile course• For those who want to achieve success in life – not justA

degree• Flexible – you may stay forA month and continue the rest of

the education by distance mode. / you may attend weekend classes

• Scholarships for those from poor economic background• Latest and constantly changing curriculum – keeping pace

with the time• Placement for those who are interested• Admissions open throughout the year • Latest and most advanced technologies, books and study

material


Components • Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad)• Meditation, spiritualisation, and self development • EsGotitial softwares for business• Business plan, Research projects• Participation in conferences / seminars• Workshops on leadership, team building etc. • Written submissions of research projects/articles / papers• Interview of entrepreneurs, writing biographies of entrepreneurs• Editing of journals / newsletters• Consultancy / research projects • Assignments, communication skill workshops• Participation in conferences and seminars• Group discussions, mock interviews, self development diaryng • Mind Power Training & writing workshop (by Dr. T.K.Jain)


Pedagogy

• Case analysis,• Articles from Harvard Business Review • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits• PreGotitations, Latest audio-visuals• Group discussions and group projects• Periodic self assessment• Mentoring and counselling• Study exchange programme (with institutions out of

India)• Rural development / Social welfare projects


Branches

• AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.


Case Studies

• We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.


Basic values at AFTERSCHO☺OL

• Share to learn more• Interact to develop yourself• Fear is your worst enemy• Make mistakes to learn • Study & discuss inA group• Criticism is the healthy route to mutual support

and help • Ask fundamental questions : why, when, how &

where?• Embrace change – and compete with yourself

only


www.afterschoool.tk social entrepreneurship for better

society