Percentages Shortcuts Formulas for CAT - EDUSAATHI

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Arithmetic - Formulae & Shortcuts Percentages 1. p % of of a number (N) = p * N 100 2. To remove %, divide by 100

a) In general, Multiplying Factor = (1  R/100) b) Final Value = (1  R/100) Initial value

3. To convert into %, multiply by 100 4. Relation b/w %ages & Fractions Fraction 1 1/2

Percentage 100

1/3 1/4 1/5 1/6 1/7 1/8

33.33 25

50

Fraction 1/9 1/10

Percentage 11.11

1/11 1/12 1/13 1/14 1/15 1/16

9.09 8.33

20 16.67 14.28 12.5

5. Percentage Change = (F  –  I)  I)  100 I (F I Final Value Initial Value) +ve if Final value > Initial Value -ve if Final value < Initial value 6. Multiplying Factor

10

7.69 7.14 6.67 6.25

c) MF = Final Value = (1  R/100) Initial value d) Tells us how many times is the Final Value in comparison to the initial value e) MF > 1 if Final value > Initial MF < 1 if Final value < Initial

Eg: A is 40% of B  A = 40/100  B  A = 0.4 B A is 40% more than B  A

 A

= B + 40/100  B

= 1.4 B

7. Base Change a) If A is r% more than B, then B is 100r % less than A 100 + r b) If A is r% less than B, then B is 100r % more than A 100 –  r  r

www.edusaathi.com c) If the price of a commodity increases/decreases  by r%,

consumption decreases/increases  by 100r / (100  r) %, given the expenditure remains same (Also known as the  product stability ratio) % Change in A

% Change in B

% Change in A

100 % ↑

50 % ↓

16.66 % ↑

14.28 % ↓

50 % ↑

33.33 % ↓

14.28 % ↑

12.5 % ↓

33.33% ↑

25 % ↓

12.5 % ↑

11.11 % ↓

25 % ↑

20 % ↓

11.11 %

20 % ↑

16.66 % ↓

10 % ↑

↑

% Change in B

10 % ↓ 9.09 % ↓

8. Successive Percentage Change a) Effective change of two successive changes of a% & b% is (a + b + ab/100)% b) In general, for more than two successive changes of a%, b%, c%... Final Value = Initial Value  (1 c/100)…

  a/100)(1   b/100)(1

SIMPLE INTEREST & COMPOUND INTEREST 1. Simple Interest = P  R  T 100 (If P & R constant, SI remains same for every year) (SI)1=(SI)2=(SI)3=(SI)4=(SI)5=======(SI)n

3. Amount = P (1 + R/100)

T

T Compound Interest = A  –  P = P (1 + R/100)  –  P

(CI)1< (CI)2< (CI)3< (CI)4 < (CI)5