# 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**

**Increase and increase respectively by x% and y% =****%****Increase and decrease respectively by x% and y% =****%****decrease and increase respectively by x% and y% =****%****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**

- x=20 is increased by 20 % , result is = 20(1.2) = 24
- Now x=24 is decreased by 50 % , result is = 24(.5) = 12
- 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**

**Increase by 10% =****=11****Increase by 20% =****=13.2****Increase by 30% =****=17.16**

Hence Final Value= 17.16