320. At the end of 1960, a student arrived at the school. When asked about his age, he replied: “My age is equal to the sum of the digits of the year of my birth.” How old is the student?
320. Given the school age, we can write the year of birth as $1900+10 x+y$. According to the problem, $1960-(1900+10 x+y)=1+9+x+y$, or $11 x + 2 y=50$ (1), from which it is clear that $x=2 x_{1}$, then $y=25-11 x_{1}$.

From the system of inequalities $\left\{\begin{array}{l}25-11 x_{1} \geqslant 0 \\ 25-11 x_{1}<10\end{array}\right.$ we find $x_{1}=2$, $x=4, y=3$.

The year of birth is 1943, age 17 years.

We can also reason as follows. According to the problem, $x$ equals 4 and 5. But from (1) it is clear that $x$ is even, therefore, $x=4, y=3$.