Two successive discounts

Statement

On a sofa priced $1200\ \text{€}$ a shop applies two successive discounts: first $20\%$, then a further $10\%$ on the already reduced price. Find the final price and the overall percentage discount.

Solution

The two discounts correspond to the factors $0{.}80$ and $0{.}90$: $1200\cdot 0{.}80 = 960, \qquad 960\cdot 0{.}90 = \boxed{864\ \text{€}}.$ Overall discount: $\dfrac{1200 - 864}{1200} = 0{.}28 = \boxed{28\%}$ (not $30\%$, since $1 - 0{.}8\cdot 0{.}9 = 0{.}28$).