### Quantitative Aptitude for Govt Exams

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**Adda247**providing some quant tricks to help aspirants.

**Percentage concept-**

**A) 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**

**B) 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**

**C) 1/5**=

**20**%,

**2/5**=

**40**%,

**3/5**=

**60**%,

**4/5**=

**80**%,

**6/5**=

**120**%

**D) 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

Note- 100-16

^{2}⁄_{3}= subtract 17 from the 100 and then subtract 3-2.**E)**

**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}

**F)****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%**

**G) 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**

**H)**

**1/10**=

**10%**

**I)**

**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

**J)**

**1/12**=

**8.33%**,

**5/12**=

**41.66**[ Recurring]

**K)**

**1/13**=

**7**

^{9}⁄_{13%}**L)**

**1/14**=

**7**,

^{2}⁄_{14}**3/14**=

**21.42%**

**M)**

**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.**

**N)**

**1/16**=6

^{4}⁄

_{16}=

**6.25**,

**3/16**=

**18.75**,

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

**31.25**

**O)**

**1/17**=

**5**

^{15}⁄_{17}**P)**

**1/18**=

**5**

^{5}⁄_{9}**Q)**

**1/19**=

**5**

^{5}⁄_{19}**R)**

**1/20**=

**5%**

**Start with some previous concepts-**

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

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

**Method 1-**let b is 100, then a is 125

**Method 2-**25%=1/4

**Best approaches-**

**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)%**

**New concept– if first value is x% more than the second value, then the second value is (x/100+x)% less than the first value**

**Now above question can be solved in mind by this formula-**

**A is 25% more than B then B is what % less than A**

**Example 2- A is 87.5% more than B then B is what % less than A**

**Best Approaches-**

**method1-**Putting value=(87.5/100+87.5)*100=(87.5/187.5)*100 is difficult task

**We can write 187.5%(100%+87.5%)=1+7/8=15/8**

**Method 2- if a is increased by (1/n)% then to compensate we have to decrease the value of b by (1/n+1)**

**Concept 2– If the first value is x% less than the second value then, second value is (x/100-x)*100**

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

**Method 1-**Putting value in the above formula 20/80*100=25%

**Method 2- here a is decreased by (1/n+1)% then to compensate we have to increase the value of b by (1/n)**

**Another approach–**

**Method 4- Ratio method **

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

**Method1-**putting value=(12.5/100-12.5)*100=(12.5/87.5)*100=14 2/7%

**Method2-**

**here (n+1)=1/8 to compensate B is increased by (n) i.e. 1/7 or 14 2/7%**

**Concept 3– If the value is first increase by x% and later decreased by x%, the net change in always a decrease which is equal to x% of x or (x)^2/100**

**Example1- A shopkeeper marks the price of his goods 12% higher than its original price. After that, he allows a discount of 12%. What is his percentage profit or loss?**

**Solution- In this case, there is always a loss.**

**Example2- If the population of a town is increased by 15% in the first year and is decreased by 15% in the next year, what effect can be seen in population?**

**Solution- there is a decrease of (15)^2/100 %=2.25%**

**Concept 4– Concept of Successive**

**a) If the value is increased successively by x% and y% then the final increase is given by**

**(x+y+xy/100)**

**b) If the value is increased by x% and decrease by y% then the final is given by**

**x-y-xy/100**

**c) if both the value is decreased by x% and y%**

**-x-y+xy/100**

**Use of successive concept- Successive is used in Percentage, Profit and loss, Compound Interest, Geometry and in data interpretation.**

**Example1- If the price is increased by 10% and the sale is decreased by 5% then what will be the effect on income?**

**Solution- Price and Sale(consumption) are inversely proportional to each other**

**If price increase then sale(consumption) decrease and vice versa**

**Successive concept in 2-D Geometry**

**Example- If one side of a rectangle is increased by 20% and the other side is decreased by 5%, find the percent value by which the area changes.**

**Solution**– % effect in the area= +20%-5%-20*5/100=14%.

**If the sides of a triangle, rectangle, square, circle, rhombus or (any 2-D figure) are increased by x%, its area is increased by**–

**[2x+ x^2/100]%**

**Example**–

**If the radius of a circle is increased by 5%, find the percentage increase in the area.**

**Solution**– % increase in its area= 5%+5+25/100=10+0.25=10.25%

**Do it for Yourself**

1. If the price of a commodity is raised by 20%, find how much percent must a household reduce his consumption of that commodity so as not to increase his expenditure.

2.If the price of sugar falls down by 10%, by how much percent must a householder increase its consumption, so as not to decrease expenditure.

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