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Quantitative Aptitude Formula Handbook

I. Arithmetic Progression.

Definition: If each term of a series differs from its preceding term by a constant, then such

a progression is called arithmetic progression.

e.g: 2,5,8,11

In the above sequence the difference between any two terms in 3.

Formula:

Consider an AP : a, (a + d), (a + 2d), (a + 3d),(a + 4d),….

1) n th term of the above sequence = Tn = a + (n – 1)d

2) Sum to n no of terms Sn = n / 2 (2a + (n – 1)d)

3) Another formula for Sn = n / 2 (first term + last term)

II. Geometric Progression.

Definition: Any progression or sequence with successive terms having a common ration is

called geometric progression.

e.g: 2,4,8,16…

In the above sequence the common ratio is 2 for any two successive terms

Formula:

Consider a GP – a, ar, ar2…. where a is the first term and r is the common ratio

4) n th term, Tn = arn-1

5) Sum to n terms, Sn = a(1 – rn)/(1-r)

6) In case r lies between -1 and +1 then Sum of all terms of the series = a/ (1 – r)

III. HCF and LCM

7) Product of two numbers = Their HCF X Their LCM

IV. Percentages

8) How to express a/b as percentage?

Ans: (a/b) x 100

9) How to express a percentage of b?

Ans: (a/100) x b

10) If the price of an item increases by A%, then the reduction in consumption so as

not to increase the expenditure is

Ans: A / (100 + A) x 100 %

11) If the price of an item decreases by A%, then the increase in consumption so as not

to decrease the expenditure is:

Ans: A / (100 – A) x 100 %

V. Profit And Loss

12) Profit = Selling Price – Cost Price

13) Loss = Cost Price – Selling Price

14) Profit Percentage = (Profit / Cost Price) x100

15) Loss Percentage = (Loss / Cost Price) x100

VI. Time And Work

16) N1 x R1 = N2 x R2 = W

Here: N = number of working men; R = rate of work done per man; D = days; W =

total work done.

VII. Boats And Streams

Let b = boat speed, s = stream speed, d = distance and t = time

17) Smooth water equation

b = d / t

18) Upstream equation

b + s = d/t

19) Downstream speed.

b – s = d/t

VIII. Simple and Compound Interest

20) For Interest Compounded Annually

Total Amount = P (1+(R/100))n

21) For Interest Compounded Half Yearly

Total Amount = P(1+(R/200))2n

22) For Interest Compounded Quarterly

Total Amount = P(1+(R/400))4n

23) Simple Interest = (Principal X Rate X Time) / 100

SI = PRT/100

Where P = capital amount, R = annual rate, T = time period in years