A man is twice as old as his wife was when the husband was as old as his wife is now. The number of years of the husband's and wife's ages, as well as the sum of these years, are in the form of aa. How old is the husband and the wife?
The ages are multiples of 11. Let the husband be $11 x$ years old, and the wife $11 y$ years old.

The husband was $11 x - 11 y$ years old $11 x - 11 y$ years ago, which is the same age as the wife is now; at that time, the wife was

$$
11 y - (11 x - 11 y) = 22 y - 11 x
$$

years old. According to the statement of the problem, currently,

$$
11 x = 2(22 y - 11 x) \quad \text{or} \quad 3 x = 4 y
$$

From this, $y = \frac{3 x}{4}$ is an integer if $x = 4 t$ and thus $y = 3 t$, where $t = 1, 2, 3, \ldots$

However,

$$
11 x + 11 y = 11(x + y) \leq 99 \text{ or } x + y \leq 9
$$

Therefore,

$$
7 t \leq 9, \text{ if } t = 1
$$

Accordingly, the husband is $11 \cdot 4 \cdot 1 = 44$ years old, and the wife is $11 \cdot 3 \cdot 1 = 33$ years old.

Ottó Varga (Bencés g. V. o. Kőszeg).