Problem 2. One third of the total quantity of a certain commodity is sold at a 10% profit, and half of the same commodity is sold at a 15% loss. By how much does the price of the remaining part of the commodity need to be increased to compensate for the loss?
Solution. Let $x$ be the quantity of the stock, then $10 \%$ of $\frac{1}{3} x$ is profit, $15 \%$ of $\frac{1}{2} x$ is loss, and $p \%$ of $x-\left(\frac{1}{3} x+\frac{1}{2} x\right)=\frac{1}{6} x$ which needs to be sold to cover the loss. According to the condition, we have:

$$
\frac{15}{100} \frac{1}{2} x-\frac{10}{100} \frac{1}{3} x=\frac{p}{100} \frac{1}{6} x
$$

From this, it follows: $p=25$.