A courier sets off from $A$ towards $B$. After a certain amount of time, the distance already covered is in the ratio of $2: 3$ to the distance yet to be covered. If the courier travels another $60 \mathrm{~km}$, the ratio of the distance already covered to the distance still to be covered becomes $6: 5$. How far is the courier from $A B$?
If the ratio of the distances is $2: 3$, then $A$ travels $2x$ and $B$ travels $3x$. If the courier travels another $60 \mathrm{~km}$, then

$$
\frac{2 x+60}{3 x-60}=\frac{6}{5}
$$

from which

$$
x=82.5
$$

and thus the distance is

$$
5 \times 82.5=412.5 \mathrm{~km}
$$

(Paunz Arthur, Pécs.)

Number of solutions: 24.