13.007. The price of the product was first reduced by $20 \%$, then the new price was reduced by another $15 \%$, and finally, after recalculation, a further reduction of $10 \%$ was made. By what total percentage was the original price of the product reduced?
## Solution.

Let $x$ be the original price of the item. After the first reduction, the price became $x-0.2x=x(1-0.2)$; after the second, $-x(1-0.2)(1-0.15)$; after the third, $-x(1-0.2)(1-0.15)(1-0.1)=0.612x$. Therefore, the total reduction from the original price is $1-0.612=0.388=38.8\%$.

Answer: $38.8\%$.