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Repeated Percentage Change

GCSELevel 6-7Edexcel iGCSE

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 \%:



Percentage decrease example:

Decrease 100 by 20 \%:



Using our knowledge on how to increase and decrease by a percentage, we can work out overall percentage changes as follows:


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:



As 0.77 is below 1, we know it is an overall decrease, so we can minus this from 1 to calculate the decrease:


The overall percentage change was a decrease of 23 \%

Level 6-7GCSEEdexcel iGCSE

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



As this is higher than 1, we can confirm it is an overall increase, and we can minus 1 to calculate the overall percentage:


Therefore, the overall percentage increase was 38 \%

Level 6-7GCSEEdexcel iGCSE

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


1.25\times0.7=0.875\\ 1-0.875=0.125

Therefore, the t-shirt had an overall percentage decrease of 12.5 \%

Level 6-7GCSEEdexcel iGCSE

Repeated Percentage Change Example Questions

15 \% increase: 1.15

40 \% decrease: 0.6


1.15\times0.6=0.69\\ 1-0.69=0.31

Therefore, the car’s value had an overall decrease of  31 \%

20 \% increase: 1.2


1.2\times1.2\times1.2=1.728\\ 1.728-1=0.728

Therefore, the ant population had an overall increase of  72.8 \%

5 \% increase: 1.05

8 \% increase: 1.08

2 \% decrease: 0.98


1.05\times1.08\times0.98=1.11132\\ 1.11132-1=0.11132

Therefore, the city’s population had an overall percentage increase of  11 \% (to the nearest whole number).

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