Quantitative Aptitude - Percentages - Formulaes and Concept Tutorial

• To find x percent of y, use the following formula

For example to find 50% of 1,

As we know 50% of 1 is 0.5 .

• If A is x% more than B, then B is less than A by

Example-

Suppose salary of x is 20% more than that of y, then the percentage by which the salary of y lesser than x?

Using Formula-

Using Normal Method

Let y salary be 100%

Then x salary is y+20 i.e 120

To find percentage by how much salary of y lesser than x

Take 120 as 100% and 100 as z%, then cross multiply it

10000 = 120 * z

z = 83.333

then the percentage by how much salary of y lesser than x is

100 – 83.33 = 16.667%

• If A is x% less than B, then B is more than A by

Example-

Suppose salary of x is 20% less than that of y, then the percentage by which the salary of y more than x?

Using Formula-

Using Normal Method

Let y salary be 100%

Then x salary is y-20 i.e 80

To find percentage by how much salary of y more than x

Take 80 as 100% and 100 as z%, then cross multiply it

10000 = 80 * z

z = 125

then the percentage by how much salary of y more than x is

125 – 100= 25%

• If value x increased by y% , then the new value is

New value =  =

Example

Suppose value 20 is increased by 50%,then the new value is

New value = 20 +  =  = 20(1.5) = 30

• If value x decreased by y% , then the new value is

new value =  =

Example

Suppose value 20 is decreased by 50%,then the new value is

New value = 20 -  =  = 20(.5) = 10

• If value a is increased or decreased successively by x% and y%, then the total % change is  %

for decrease use –ve , for increase use +ve

1. Increase and increase respectively by x% and y% =  %
2. Increase and decrease respectively by x% and y% =  %
3. decrease and increase respectively by x% and y% =  %
4. decrease and decrease respectively by x% and y% =  %

If result is –ve then total % change is decreased.

If result is +ve then total % change is increased.

Example-

Suppose x = 20 increased by 20 % and decreased by 50 %, then total % change is

Using Formula

Percentage change=  = -40 %

Final value is decreased by 40%

Using  Normal Method

1. x=20 is increased by 20 % , result is = 20(1.2) = 24
2. Now x=24 is decreased by 50 % , result is = 24(.5) = 12
3. Let 20 is 100%,then 12 is ,solve by cross multiply

a = 60%

Then the change in value is 100 – 60 = 40% decreased.

• If number a is increased successively by x% followed by y% and then by z%, then the final value will be:

Final value =

Using Formula

Suppose value 10 is increased by 10%, followed by 20% ,then by 30%. Then the final value will be

Final value =  =   = 17.16

Using Normal Method

1. Increase by 10% = =11
2. Increase by 20% = =13.2
3. Increase by 30% = =17.16

Hence Final Value= 17.16