Successive discounts

Statement

On Monday an item costs full price. On Tuesday the shop reduces all prices by $25\%$. On Wednesday, by what percentage must it reduce the Tuesday prices so that each item costs $60\%$ of the Monday price?

Solution

Set the Monday price equal to $1$ (i.e. $100\%$).

Tuesday. Reduced by $25\%$: the new price is $1 - 0.25 = 0.75$.

Wednesday target. We want to reach $0.60$ starting from $0.75$. The required reduction, as a percentage of the Tuesday price, is $\frac{0.75 - 0.60}{0.75} = \frac{0.15}{0.75} = 0.20 = 20\%.$ Check: $20\%$ of $0.75$ is $0.15$, and $0.75 - 0.15 = 0.60$. Correct. $\boxed{20\%}$