Formula Booklet New

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Quantitative Aptitude

Formula Booklet

Corporate & International Relations


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Formula Booklet

2 Corporate & International Relations

1. Averages

Simple averages =

Weighted Average =

Geometric Mean =

Harmonic Mean =

For two numbers, Harmonic Mean =

2. Percentage Change

Change % = %

Total Successive Change% = %

3. Interest

Simple Interest =

Compound Interest =

Population after n years P =

4. Growth

Growth% = %

SAGR or AAGR = %

CAGR = %

[Here, S. A. G. R. = Simple Annual Growth Rate, A. A. G. R. = Average Annual Growth Rate and C. A. G. R. = Compound

Annual Growth Rate]

5. Profit and Loss

Profit = SP CP

Loss = CP SP

Percentage Profit =

Percentage Loss =

6. False Weights

If an item is claimed to be sold at cost price, using false weights, then the overall percentage profit is given by


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Percentage Profit =

7. Discount

Discount = Marked Price Selling Price

Discount Percentage =

8. Buyxand Get yFree

If articles worth Rs.xare bought and articles worth Rs. yare obtained free along withxarticles, then the discount is equal

to yand discount percentage is given by

Percentage discount =

9. Successive Discounts

When a discount ofa% is followed by another discount ofb%, then

Total discount =

10. Ratios

Ifa:b = c:d, then a: b = c:d= (a + c): (b + d) If 0 b>0, then for a positive quantityx,

11. Proportions

If a: b:: c:d or , then

Alternendo Law

Invertendo Law

Componendo Law

Dividendo Law

Componendo and Dividendo Law

If , then

and p, q, r are real numbers, then


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12. Successive Replacement

Wherexis the original quantity, yis the quantity that is replaced and n is the number of times the replacement process is

carried out.

13. Alligation Rule

The ratio of the weights of the two items mixed will be inversely proportional to the deviation of attributes of these two

items from the average attribute of the resultant mixture.

Alligation Cross:

x1 x2

x

x2- x : x x1

w1 w2

14. Time, Speed and Distance

Speed = Distance / Time

Important Conversion Factors:

1 km/hr = m/s and 1 m/s = km/hr

15. Average Speed

Average = =

A man travels first half of the distance at a speed , second half of the distance at a speed then, Average Speed

[Average speed is given by harmonic mean of two speeds] Savg =

If the time is constant, then average speed is given by arithmetic mean of two speeds: Savg =


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16. Relative Speed

For Trains

Time =

For Boats and Streams

Sdownstream = Sboat + Sstream

Supstream = Sboat - Sstream

Sboat =

Sstream =

17. Time and Work/Pipes and Cisterns

Number of days to complete the work =

[This is our general formula to solve time & work problems. It is also known as Work Equivalence Method]

18. Application of H.C.F.

The greatest natural number that will dividex, yand z leaving remainders r1, r2 and r3, respectively, is the H.C.F. of

(xr1), (yr2) and (z r3)

19. Application of L.C.M.

The smallest natural number that is divisible byx, yand z leaving the same remainder rin each case is the L.C.M. of

(x, yand z) + r

20. H.C.F. and L.C.M. of Fractions

H.C.F of fractions =

L.C.M of fractions =

[Express all numbers as fractions in its simplest form]

21. Properties of Surds


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22. Law of Indices

If a and b are non zero rational numbers and m and n are rational numbers, the

If , then m = n

If and m 0, then a = b if m is odd and a = b if m is even

23. Laws of Logarithms

If

If

24. Binomial Theorem

If n is a natural number that is greater than or equal to 2, then according to the binomial theorem:

(x+a)n

=n

coxn

a0

+n

c1xn-1

a1

+n

c2xn-2

a2

+. +n

cnx0

an

Here,


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25. Roots of Quadratic Equation

The two roots of the equation, ax2+bx+c =0 are given by:

26. Algebraic Formulae

(a + b) (a b) = a2

b2

(a + b)2

= a2

+ 2ab + b2

(a b)2

= a2 2ab + b

2

(a + b + c)2

= a2

+ b2

+ c2

+ 2ab + 2bc + 2ca

(a + b)3

= a3

+ 3a2b + 3ab

2+ b

3

(a b)3

= a3 3a

2b + 3ab

2 b

3

a3

+ b3

= (a + b) (a2 ab + b

2)

a3 b

3= (a b) (a

2+ ab + b

2)

a3

+ b3

+c3 3abc = (a+ b + c) (a

2+ b

2+ c

2 ab bc ac)

27. Arithmetic Progression

28. Geometric Progression

29. Harmonic Progression

30. Sum of Important Series

Sum of first n natural numbers


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Sum of the squares of the first n natural numbers

Sum of the cubes of the first n natural numbers

=

31. Factorial

n! = 1 2 3 (n 1) n

n! = n (n 1)!

32. Permutations

33. Combinations

Important Properties:

34. Partition Rule

Number of ways of distributing n identical things among rpersons when each person may get any number of things

=

35. Probability

Probability of an event =

Odds in favour =

Odds against =


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36. Pythagoras Theorem

For right triangle ABC

AC

2

= AB

2

+BC

2

For acute triangle ABC

AC2

= AB2

+ BC2 2 (BC) (BD)

For obtuse triangle ABC

AC2

= AB2

+ BC2

+ 2*BC*BD


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37. Area of Triangle

When lengths of the sides are given

Area =

Where, semi perimeter (s) =

When lengths of the base and altitude are given

Area =

When lengths of two sides and the included angle are given

Area =


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For Equilateral Triangle

Area =

For Isosceles Triangle

Area =

38. Apollonius Theorem

If AD is the median, then:

AB2

+ AC2

= 2(AD2

+ BD2)


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39. Angle Bisector Theorem

If AD is the angle bisector for angle A, then:

40. Area of Quadrilateral

For Cyclic Quadrilateral

Area =

Where, semi perimeter (s) =

If lengths of one diagonal and two offsets are given

Area =

If lengths of two diagonals and included angle are given

Area =


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For Trapezium

Area =

For Parallelogram

Area = bh

For Rhombus

Area =

For Rectangle

Area = lb


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For Square

Area = a2

41. Polygon

Number of Diagonals =

The sum of all the interior angles =The sum of all exterior angles = 360

42. Area of Regular Hexagon

Area =

43. Circle


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Circumference C =

Area (A) =

Length of Arc (l) = , where is in degrees.

Area of Sector = , where is in degrees.

Perimeter of Sector =

44. Ellipse

If semi-major axis (OD) = a and semi-minor axis (OA) = b,

Perimeter of the ellipse

Area of the ellipse

45. Trigonometric Ratios

For a right triangle, ifP is the length of perpendicular, B is the length of base, H is the length of hypotenuse and is

the angle between base and hypotenuse,


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46. Distance between Points

Distance between two points and is given by

AB =

47. Right Prism

Lateral Surface Area (L.S.A.) = Perimeter of base height

Total Surface Area (T.S.A.) = L.S.A. + 2 Area of base

Volume (V) = Area of base height

48. Cuboid

S.A. = 2(lh + bh)

T.S.A. = 2(lh + bh + lb)


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Volume (V) = lbh

Body Diagonal (d) =

49. Cube

L.S.A = 4a2

T.S.A = 6a2

Volume (V) =a3

Body Diagonal (d) =

50. Cylinder

Curved Surface Area (C.S.A.) = 2rh

T.S.A. = 2rh + 2r2

Volume (V) = r2h


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51. Right Pyramid

L.S.A = Perimeter of Base Slant Height

T.S.A = L.S.A + Area of base

Volume (V) = Area of Base Height

52. Cone

C.S.A. = rl

T.S.A. = rl + r2

Volume (V) =

Slant height (l) =


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53. Frustum of a cone

Volume (V) =

54. Sphere

C.S.A. = 4r2

T.S.A. = 4r2

Volume (V) =

55. Hemisphere

C.S.A. = 2r2

T.S.A. = 3r2

Volume (V) =


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56. Spherical shell

T.S.A =

Volume (V) =

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