13.353. When multiplying two positive numbers, one of which is 75 more than the other, the product was mistakenly obtained as 1000 less than the true product. As a result, when dividing (during verification) the incorrect product by the smaller of the multipliers, a quotient of 227 and a remainder of 113 were obtained. Find both numbers.
Solution.

Let $x, y$ be the required numbers, $z$ be the erroneous product of numbers $x$ and $y$.

According to the condition, we have the system $\left\{\begin{array}{l}x-y=75, \\ x y=z+1000 \\ z=227 y+113,\end{array}\right.$ from which $x=234, y=159$.

Answer: 159 and 234.