Problem 1. A barrel is filled with water to $\frac{5}{6}$ of its volume. If another 10 liters of water are added to the barrel, it will be filled to $\frac{7}{8}$ of its volume. How many liters of water does the barrel hold?
Solution. Let the barrel collect $x$ liters of water. From the condition of the problem, we have $\frac{5}{6} x+10=\frac{7}{8} x$, that is, $10=\left(\frac{7}{8}-\frac{5}{6}\right) \cdot x$, or $10=\frac{1}{24} \cdot x$, from which $x=24 \cdot 10=240$. Therefore, the barrel collects 240 liters of water.