Number

Percentages and Chain Percentages

Use percentage multipliers to handle repeated changes efficiently.

Multiplier method

Increase by r%\[\times\left(1+\frac r{100}\right)\]
Decrease by r%\[\times\left(1-\frac r{100}\right)\]

Worked example

A price of €80 is reduced by 10%, then reduced again by 15%. Find the final price.

\[80\times0.90\times0.85=61.20\]

The final price is €61.20.

Single equivalent change

Increase by 20%, then decrease by 5%:

\[1.20\times0.95=1.14\]

The single equivalent change is a 14% increase.