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.