2. The age of a person this year is equal to the sum of the digits of their birth year. How old is the person?
Solution. The person is at most $9+9+9+9=36$ years old, which means they were born in the $X X$ century, i.e., in the $\overline{19 x y}$ year. According to the condition of the problem, we have

$$
1+9+x+y=1991-(1000+900+10 x+y)
$$

i.e.

$$
11 x+2 y=81
$$

from which we get $x=7, y=2$. Therefore, the person was born in 1972 and is now $1+9+7+2=19$ years old.