$A$ said to $B$: give me $\frac{1}{4}$ of your money $\mathrm{s}$ and I can buy $6 \mathrm{hl}$ of wine. $B$ replied: If you give me $\frac{1}{5}$ of your money, I can buy $8 \mathrm{hl}$ of wine. A few days later, they met again, after one had won 46 crowns and the other had lost the same amount. Then $A$ said to $B$: If you give me $\frac{1}{3}$ of your money, I can buy $30 \mathrm{hl}$ of wheat. $B$ replied: If you give me $\frac{1}{3}$ of your money, I can buy $36 \mathrm{hl}$ of wheat. How much money did each of them have? How much did $1 \mathrm{hl}$ of wine and $1 \mathrm{hl}$ of wheat cost?
At the first meeting, $A$ had $x$ crowns, and $B$ had $y$ crowns; at the second meeting, $A$ had $(x+46)$ crowns, and $B$ had $(y-46)$ crowns.

Let the price of $1 \mathrm{hl}$ of wine be $z$ crowns, and the price of $1 \mathrm{hl}$ of wheat be $u$ crowns. According to the problem, we have:

$$
x+\frac{y}{4}=6 z
$$

$$
x+46+\frac{y-46}{3}=30 u
$$

$$
y-46+\frac{x+46}{3}=36 u
$$

By rearranging the equations and eliminating $z$ from equations (1) and (2), and $u$ from equations (3) and (4), we get:

$$
17 x-10 y=0
$$

and

$$
13 x-9 y=-1012
$$

from which

$$
x=440, y=748, z=104.5, u=24
$$

(Jánosy Gyula, Budapest.)

The problem was also solved by: Bánó L., Cukor G., Füstös P., Harsányi Z., Heimlich P., Kiss J., Makó E., Paunz A., Schlesinger Gy., Schuster Gy., Steiger J., Tóth B.