Quant Hacks| Percentage concept

In competitive exam percentage to fraction value, up to 20 is asked.
(A) 1/2= 50/100= 50%, 
3/2= 3*50%=150%,
5/2= 5*50%=250%


(B) 1/3= 1/3*100=33.33%( Recurring decimal)
2/3= 2*33.33%=66.66%,
4/3= 4* 33.33 but this is not easy we can write it as (1+1/3)*100=100%+33.33=133.33

(C) 1/4= 25%
3/4=3*25%=75%,
5/4 is improper fraction, split it into= (1+1/4)*100=100%+25%=125%
6/4= 3/2*100=150% or if you know table of 25 then directly 6*25=150
7/4= split it (1+3/4)*100=175% or 25*7=175

(D) 1/5= 20%,
2/5=40%,
3/5=60%,
4/5=80%,
6/5= 120%

(E) 1/6=16.66% or 16²⁄₃
2/6=1/3=33.33%,
5/6=5*16.66=83.33% or we can break it into (1-1/6)*100=100%-16²⁄₃=83¹⁄₃
7/6=(1+1/6)=116.66%


Note- 100-16²⁄₃= subtract 17 from the 100 and then subtract 3-2.
all the subtraction in fractions happens as above

(F) 1/7=14.28% or 14²⁄₇,
2/7=28.56 %
3/7= we multiply 3*14 2/7= 3*(14+2/7)%= 42%+6/7%=42.85
4/7=4*(14²⁄₇)=56+8/7=57 1/7
6/7= 1-1/7=100-14²⁄₇=85⁵⁄₇

(G) 1/8= 12.5%,
3/8=37.5%,
5/8= 62.5%,
7/8=(1-1/8)=100%-12.5=87.5%
9/8=(1+1/8)*100=112.5%

(H). 1/9= 11.11%,
2/9=22.22,
4/9= 44.44%,
5/9=55.55%,
6/9=66.66%
[ Note the trend]- same value before and after decimal

(I). 1/10=10%

(J). 1/11=9.09%,
 2/11= 18.18%, 3/11=27.27%, 4/11= 36.36 [ Note the trend]- same value before and after decimal

K. 1/12=8.33%, 5/12= 41.66 [ Recurring]

L. 1/13= 7⁹⁄_13%

M. 1/14=7²⁄₁₄, 3/14=21.42%

N. 1/15=6¹⁰⁄₁₅=6²⁄₃=6.66 or divide and multiply by 2 in numerator and denominator=2/30, 4/15=8/30

Note- if denominator has 5 in its unit place make it 10.

O. 1/16=6⁴⁄₁₆=6.25, 3/16=18.75, 5/16= 5*(6.25)=31.25

P. 1/17=5¹⁵⁄₁₇

Q. 1/18=5⁵⁄₉

R. 1/19=5⁵⁄₁₉

S. 1/20= 5%

Basic of Percentage and Use of percentage to Fraction value

1. a is what % of b 

2. b is what % of a

3. what % of b is a

4. what % of a is b

5. a is what % more than b 

6. b is what % more than a

Solution and concept-

the main confusion among students is what is the denominator in the above questions. Many times student get confused and wasted a lot of time 

the number or value always after “of “and “than” comes in denominator

1. a is what % of b= a/b*100[ b is in denominator ], 

the same b is what % of a, here a comes after of so a is in the denominator

=b/a*100

2. what % of b is a= b comes after “of “ so here a/b*100

3. a is what % more than b[ this statement is very important we see many times in data interpretation]

here b is after “than”.

write this as- (a-b)/b*100.

or you first find ratio between a and b then compare both.

example1– a is 25% more than b means

if b=100 then a=125

or if you know percentage to fraction value then make easier to find ratio

25%= 1/4. 

if b=4 then a is 25% more than b i.e.1/4*4=1 then the value of a=1+4=5

now a(5) is more than b(4)=(5-4)/4*100=20%

more example to familiarise you with the ratio method-

Concept– a is 40% more than b

we write it as 40%= 2/5

when value of b=5 then 40% of 5=2/5*5=2

value of a= 5+2=7

ratio between a/b=7/5

Concept- a is 87.5% more than b

we write 87.5%= 100%-12.5%

100%=1

12.5%=1/8

1-1/8=7/8

now the value of b=8 then 7/8*8=7

a is 87.5% more than b=15

ratio of a and b=15:8

Now the implementation of the above concepts –  

Example1- A is 25% more than b, then b is what % less than a

method 1– let b is 100, then a is 125

b is what % less than a = 125-100/125=25/125*100=20%

method 2– 25%=1/4

if b=4 then 1/4*4=1

a=5

a/b=5/4 then b is what % less than a=1/5*100=20%

method 3- shortcut

if a is increased by (1/n)% then to compensate we have to decrease the value of b by (1/n+1)

increase of 25% =1/4 here n=4  then b is decreased by 1/(4+1) i.e. 1/5 or 20%

Example 2– a is 87.5% more than b then b is what % less than a

method1– let b=100, then a is 187.5 here calculation becomes difficult 

method2– 87.5%= 7/8

if b=8 then 7/8*8=7

a=15, b=8, b is 7 less than a= 7/15*100

method 3– if a is increased by (1/n)% then to compensate we have to decrease the value of b by (1/n+1)

here a is increase by1/ n=1/(8/7) then b is decreased by (1/(8/7+1)

i.e. b is decreased by 7/15

Example 3– A is 7.7 % more than b, then b is what percent less than a

method 1. ratio method is difficult to solve

method 2-

here this method plays a vital role- if a is increased by (1/n)% then to compensate we have to decrease the value of b by (1/n+1)

if you remember we write 7.7%=1/13

here a is increased by 1/13 then b is decreased by 1/14.

Now Examples of first we decrease than Increase

Examples1. when A is 20% less than B then B is what % more than A.

method 1– let a=80, b=100 then 20/80*100=25%

method 2– ratio method 

20%=1/5 when b is 5 then 5*1/5=1

a is 20% less than b then a= 4

we write a/b=4/5, 1/4*100=25%

method3– here a is decreased by (1/n+1)% then to compensate we have to increase the value of b by (1/n)

here (n+1)=5 then to compensate we have to increase the value by (n) i.e. 4 so b is more than a by 25%.

Example2- A is 12.5% less than B then B is what % more than A

method1. Solve it by shortcut

here (n+1)=1/8 to compensate B is increased by (n) i.e. 1/7 

Example3. A is 16 2/3 more than B and 20% of C. B is what % of C

Ratio method- B= 6, A=7—(1)

and C= 5 then A= 1—(2)

compare ratio multiply equ 2 by 7

A=7, B=6, C=35

=6/35*100

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