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 $20 \%$ :

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=0.23

The 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=0.38

Therefore, 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=0.125

Therefore, 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=0.31

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

Save your answers with

Gold Standard Education

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=0.728

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

Save your answers with

Gold Standard Education

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: