##### Increase and decrease concept

#### Problem 1: If the radius of the right circular cylinder is increased by 40% and its height is reduced by 37.5% then find the percentage change in its volume?

Solution: Radius increased to 40% =

Height decreased to 37.5%=

Volume of a cylinder =

Actual volume =

Radius increased=5+2=7

Height decreased = 8-3 =5

Changed volume=

% change in its volume =

=

=22.5

##### Problem 2: If the length of the rectangle is increased by 20% and the breadth of the rectangle is decreased by 20% find the percentage change in its area?

Solution: Length increased to 20%

Breadth decreased to 20%

Area of the rectangle = Length * Breadth

Actual area = 10*10 = 100

Changed area = 12*8 =96

% change in the area =

=

=-4%

Here ‘-‘ indicates area decreased to 4%

Shortcut method: Direct formula = = 4

Note:

- The above method is applicable when there is increase or decrease in the value of 10%,20%,30,%40%,50%,60%, etc.
- If such values occur follow first problem method. It is not applicable when the fractional values occur.
- The fractional values like 37.5%,%, etc., If such values occur follow first problem method.