Quant Hacks| Percentage concept

Quantitative Aptitude is hard in most cases especially in exams like Banks and Insurance. Many Banks exam has a two-tier examination pattern i.e., Prelims and Mains. Most of them have changed their exam patterns and set a sectional timing of 20 minutes on each section. Quantitative aptitude is important for every exam because proper strategy and enough practice can help you score full marks in this section. There may not be assured in the language section and you may be stuck while solving reasoning questions but quants is a scoring subject and assure full marks if the calculation is correct.
So to help you ace the quants and to save your precious time during exam hours Adda247 providing some quant tricks to help aspirants.

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 1623
2/6=1/3=33.33%,
5/6=5*16.66=83.33% or we can break it into (1-1/6)*100=100%-1623=8313
7/6=(1+1/6)=116.66%


Note- 100-1623= subtract 17 from the 100 and then subtract 3-2.

all the subtraction in fractions happens as above

(F) 1/7=14.28% or 1427,
2/7=28.56 %
3/7= we multiply 3*14 2/7= 3*(14+2/7)%= 42%+6/7%=42.85
4/7=4*(1427)=56+8/7=57 1/7
6/7= 1-1/7=100-1427=8557

(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= 7913%

M. 1/14=7214, 3/14=21.42%

N. 1/15=61015=623=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=6416=6.25, 3/16=18.75, 5/16= 5*(6.25)=31.25

P. 1/17=51517

Q. 1/18=559

R. 1/19=5519

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-
Concepta 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 2a 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 
method287.5%= 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 3A 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