Problem 2. The grandfather and the grandson together are 65 years old. How old is the grandfather, and how old is the grandson if it is known that the grandson has as many months as the grandfather has years?
Solution. First method. A year has 12 months, so the grandfather is 12 times older than the grandson. If the grandson is $x$ years old, then the grandfather is $12 x$ years old, hence

$$
12 x+x=65, \quad 13 x=65 ; x=65: 13 ; x=5
$$

i.e., the grandson is 5 years old, and the grandfather is 60 years old.

Second method. A year has 12 months, so the grandfather is 12 times older than the grandson.

$$
\begin{aligned}
& 1 \cdot 12=12,1+12 \neq 65 \\
& 2 \cdot 12=24,2+24 \neq 65 \\
& 3 \cdot 12=36,3+36 \neq 65 \\
& 4 \cdot 12=48,4+48 \neq 65 \\
& 5 \cdot 12=60,5+60=65
\end{aligned}
$$

Thus, the grandson is 5, and the grandfather is 60 years old.