# CLASS-7PERCENTAGE OF CHANGE

Percentage of Change

A change in a quantity can be expressed as a percentage of the quantity. Knowing the change percent helps us compare changes, for example, if the price of a shirt increase from \$ 120 to \$ 160 in some one year and in subsequent year from \$ 160 to \$ 200, we can compare the increase in price in the two years only if we know the percentage of increase in each of the two years.

Increase in quantity

Percentage of increase = -------------------------  X  100

Original quantity

Percentage of increase

Increase in quantity = -----------------------  X Original quantity

100

=  percentage as fraction X original quantity

So, the new quantity  = original quantity + increase

= original quantity + original quantity X percentage as fraction

= original quantity ( 1 + percentage as fraction )

When the quantity decrease, change the ‘+’ sign to ‘-‘

Example –

1) If the number 100 is increased by 40 %, then find the new number. What will be the new number if 100 is decreased by 50 %

Ans.) As per the rules and given condition –

So, the new quantity = Original quantity (1 + Percentage as a Fraction)

40

=   100  ( 1 + --------- )

100

100 +  40

=    100  X  ---------------

100

=   100 +  40  =  140         (Ans.)

As per the rules and given condition –

So, the new quantity = Original quantity (1+ Percentage as a Fraction)

50

=   100  ( 1 - ---------- )

100

100 -  50

=    100  X  -------------

100

=   100 -  50  =  50         (Ans.)