Initial price with two changes

Statement

The price of a product rises by $20\%$ and then falls by $15\%$. If the final price is $102\ \text{€}$, what was the initial price?

Solution

Let $P_0$ be the initial price; the final price is $P_0\cdot 1{.}20\cdot 0{.}85 = 1{.}02\,P_0$. $1{.}02\,P_0 = 102 \ \Rightarrow\ P_0 = \frac{102}{1{.}02} = \boxed{100\ \text{€}}.$