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.)