Question

A shop has a sale that offers 20% off all prices.

On the final day they reduce all the sale prices by 25%.
Linz buys a radio on the final day.
Work out the OVERALL percentage reduction on the price of the radio.

Answer 1

The overall percentage reduction on the price of the radio is 40% of its original price.

Explanation:

If a price is reduced by 20%, then it becomes 80% of its original price, since 100% - 20% = 80%.

If the reduced price is then reduced by 25%, then it becomes 75% of its reduced price, since 100% - 25% = 75%.

Therefore, we need to find 75% of 80% and subtract this from 100% to determine the overall percentage reduction.

`\begin{aligned}\implies 100\%-(75\%\; \textsf{of}\; 80\%)&=1-(0.75 * 0.8)\\&=1-0.6\\&=0.4\\&=40\%\end{aligned}`

Therefore, the overall percentage reduction on the price of the radio is 40% of its original price.

For example, if the original price of the radio is $150, then when it is reduced by 20% it costs $120. If it is then reduced again by 25% it costs $90. As $150 reduced by 40% is $90, this proves that the overall percentage reduction is 40%.