# 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-**

**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

**16**

^{2}⁄_{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%-16**=83

^{2}⁄_{3}^{1}⁄

_{3}

**7/6**=(1+1/6)=

**116.66%**

**Note- 100-16**

^{2}⁄_{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

**14**,

^{2}⁄_{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*(14

^{2}⁄

_{7})=56+8/7=

**57 1/7**

**6/7**= 1-1/7=

**100-14**=

^{2}⁄_{7}**85**

^{5}⁄_{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**=

**7**

^{9}⁄_{13%}**M**.

**1/14**=

**7**,

^{2}⁄_{14}**3/14**=

**21.42%**

**N**.

**1/15**=

**6**=

^{10}⁄_{15}**6**=6.66 or divide and multiply by 2 in numerator and denominator=2/30, 4/15=8/30

^{2}⁄_{3}**Note- if denominator has 5 in its unit place make it 10.**

**O**.

**1/16**=6

^{4}⁄

_{16}=

**6.25**,

**3/16**=

**18.75**,

**5/16**= 5*(6.25)=

**31.25**

**P**.

**1/17**=

**5**

^{15}⁄_{17}**Q**.

**1/18**=

**5**

^{5}⁄_{9}**R**.

**1/19**=

**5**

^{5}⁄_{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

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