## 25. School

In all the classes of one school, the same number of students studied. After a fire, six classes of the school became unsuitable for lessons, and therefore, five more students had to be added to each class where lessons were held. But then, due to water damage from the fire hoses, another ten classes were recognized as being in a threatened condition. Then, fifteen more students had to be added to each class that remained in good condition.

How many students are there in this school?
25. Let $c$ be the number of students in each class before the fire, and $n$ be the number of classes at that time. Then the following relationships hold:

$$
\begin{gathered}
n c=(n-6)(c+5) \\
n c=(n-16)(c+20)
\end{gathered}
$$

From these two equations, it follows that

$$
\begin{gathered}
-6 c+5 n-30=0 \\
-16 c+20 n-320=0
\end{gathered}
$$

Therefore, $c=25, n=36$.

Thus, the number of students in the school is

$$
n c=36 \cdot 25=900
$$