42 (1284). How old is the brother and how old is the sister if 2 years ago the brother was twice as old as the sister, and 8 years ago - five times as old?
Solution. Method I. Let the current age of the sister be $x$ years, and the brother's age be $y$ years. According to the problem, we set up the system of equations:

$$
\left\{\begin{array}{l}
y-2=2(x-2) \\
y-8=5(x-8)
\end{array}\right.
$$

from which we find $x=10, y=18$.

Method II. Let 2 years ago the sister was $x$ years old, and the brother was $2x$ years old. Eight years ago, the sister was $(x-6)$ years old, and the brother was $(2x-6)$ years old. According to the problem, we have:

$$
2 x-6=5(x-6), \text { from which } x=8, 2 x=16
$$

Therefore, the sister is currently 10 years old $(8+2=10)$, and the brother is 18 years old $(16+2=18)$.

Answer: 18 years, 10 years.