# Repeated Percentage Change

GCSELevel 6-7Edexcel iGCSE

## 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 $23 \%$

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: $1.15$

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 $38 \%$

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: $0.7$

Overall:

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

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: $0.6$

Overall:

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

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

$20 \%$ increase: $1.2$

Overall:

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

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

$5 \%$ increase: $1.05$

$8 \%$ increase: $1.08$

$2 \%$ decrease: $0.98$

Overall:

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

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

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