13.062. An apprentice turner is machining pawns for a certain number of chess sets. He wants to learn to produce 2 more pawns per day than he does now; then he would complete the same task 10 days faster. If he could learn to produce 4 more pawns per day than he does now, the time required to complete the same task would be reduced by 16 days. How many chess sets does this apprentice supply with pawns, if 16 pawns are needed for each set?
## Solution:

Let the turner provide $x$ sets of chess pieces. He completes the task in $y$ days. According to the problem,

$$
\left\{\begin{array}{l}
\left(\frac{16 x}{y}+2\right)(y-10)=16 x \\
\left(\frac{16 x}{y}+4\right)(y-16)=16 x
\end{array}, \text { from which } x=15\right.
$$

Answer: 15.