I am twice as old as you were when I was as old as you are now. But when you are as old as I am now, the sum of our ages will be 140. How old are you, and how old am I?
Solution: If you are $x$ years old and I am $y$ years old, then $x-y$ years ago, I was half as old as you are now, that is,

$$
x=2[y-(x-y)]
$$

from which

$$
3 x=4 y
$$

$x-y$ years from now, the sum of our ages will be 140, so

$$
x+(x-y)+y+(x-y)=140
$$

or

$$
3 x-y=140
$$

From (1) and (2), $x=62 \frac{2}{9}$ and $y=46 \frac{2}{3}$, which means you are $62 \frac{2}{9}$ years old and I am $46 \frac{2}{3}$ years old.

(Pál Sárközy, Pannonhalma.)

The problem was solved by: Babocsai G., Bayer N., Csada I., Cukor G., Dénes M., Erdős V., Frankl F., Fried E., Grossberger Z., Grün E., Kirchknopf E., Kiss J., Klein G., Koffler B., Kovács Gy., Lengyel P., Miklóssy K., Neumann L., Paunz A., Putnoky L., Rosenthal M., Sebestyén I., Steiner L., Szilárd V., Viola R.