$A$'s money is in the ratio of $8: 5$ to $B$'s money. If $A$ loses $50 \mathrm{~K}$, and $B$ wins $100 \mathrm{~K}$, then the ratio of their money becomes $5: 4$. How much money did each have?
Let $A$ have $8 \times K$, then $B$ has $5 \times K$.

In the context of the problem:

$$
8 x - 50 : 5 x + 100 = 5 : 4
$$

from which

$$
x = 100
$$

Therefore, $A$ has 800 and $B$ has $500 \, K$.

(Fried Ernö, Budapest.)

Number of solutions: 41.