13.315. The initial cost price of a unit of product was 50 rubles. During the first year of production, it increased by a certain percentage, and during the second year, it decreased (relative to the increased cost price) by the same percentage, as a result of which it became 48 rubles. Determine the percentages of the increase and decrease in the cost price of a unit of product.
## Solution.

Let the cost of a unit of production increase by x percent.

After the increase, the cost became $50+\frac{x}{100} \cdot 50=50+\frac{x}{2}$, and after the decrease - $\left(50+\frac{x}{2}\right)-\frac{x}{100} \cdot\left(50+\frac{x}{2}\right)=\left(50+\frac{x}{2}\right)\left(1-\frac{1}{100}\right) \cdot$ According to the condition, we have $\left(50+\frac{x}{2}\right)\left(1-\frac{x}{100}\right)=48$, from which $x=20 \%$.

Answer: $20 \%$.