Repeated Percentage Change
Repeated Percentage Change Revision
Repeated Percentage Change
A repeated percentage change question involves calculating the overall percentage change that has resulted from more than one consecutive percentage changes.
Calculating Percentage Change
Repeated percentage changes can include percentage increases or percentage decreases:
Percentage increase example:
Increase 100 by 20 \%:
100\times1.2=120
Percentage decrease example:
Decrease 100 by 20 \%:
100\times0.8=80
Using our knowledge on how to increase and decrease by a percentage, we can work out overall percentage changes as follows:
Example:
Calculate the overall percentage change when an increase of 10 \% is followed by a decrease of 30 \%.
An increase of 10 \% would mean multiplying by 1.1, and a decrease of 30 \% would mean multiplying by 0.7.
To find the overall change, we need to multiply these together:
1.1\times0.7=0.77\\
As 0.77 is below 1, we know it is an overall decrease, so we can minus this from 1 to calculate the decrease:
1-0.77=0.23The overall percentage change was a decrease of 23 \%
Example 1
Calculate the overall percentage increase when 70 is increased by 20 \%, and then increased by a further 15 \%
[2 marks]
The quickest way to calculate this is by using the percentage changes directly:
20 \% increase: 1.2
15 \% increase: 1.15
Overall:
1.2\times1.15=1.38\\As this is higher than 1, we can confirm it is an overall increase, and we can minus 1 to calculate the overall percentage:
1.38-1=0.38Therefore, the overall percentage increase was 38 \%
Example 2
In a shop, a t-shirt is firstly increased in price by 25 \%, but as it did not sell well at this new price, the price was later decreased by 30 \%. Calculate the overall percentage change.
[2 marks]
25 \% increase: 1.25
30 \% decrease: 0.7
Overall:
1.25\times0.7=0.875\\ 1-0.875=0.125Therefore, the t-shirt had an overall percentage decrease of 12.5 \%
Repeated Percentage Change Example Questions
Question 1: The value of a car increases by 15 \% in one year, but then decreases by 40 \% in the next. Calculate the overall percentage change in the car’s value over the 2 years.
[2 marks]
15 \% increase: 1.15
40 \% decrease: 0.6
Overall:
1.15\times0.6=0.69\\ 1-0.69=0.31Therefore, the car’s value had an overall decrease of 31 \%
Question 2: A population of ants increases by 20 \% each year. Calculate the overall percentage increase of ants over 3 years.
[2 marks]
20 \% increase: 1.2
Overall:
1.2\times1.2\times1.2=1.728\\ 1.728-1=0.728Therefore, the ant population had an overall increase of 72.8 \%
Question 3: The number of people in a city had an increase of 5 \% in January, an increase of 8 \% in February, and then a decrease of 2 \% in March.
Calculate the overall percentage change in the 3 months, to the nearest whole number.
[3 marks]
5 \% increase: 1.05
8 \% increase: 1.08
2 \% decrease: 0.98
Overall:
1.05\times1.08\times0.98=1.11132\\ 1.11132-1=0.11132Therefore, the city’s population had an overall percentage increase of 11 \% (to the nearest whole number).
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