A body's weight is $p$. The weight of this body in a liquid of density $d_{1}$ is $p_{1}$, and in a liquid of density $x$ is $p_{2}$. What is $x$, and what is the density $d$ of the body?
The weight loss of a body immersed in a fluid is the same as the weight of an equal volume of the fluid; however, the weights of equal volumes of bodies are in the same ratio as their densities, thus

$$
p:\left(p-p_{1}\right)=d: d_{1}
$$

from which

$$
d=\frac{d_{1} p}{p-p_{1}}
$$

Applying the same consideration to the second fluid:

$$
p:\left(p-p_{2}\right)=d: x
$$

from which

$$
x=d \frac{p-p_{2}}{p}=d_{1} \cdot \frac{p-p_{2}}{p-p_{1}} .
$$

(Sándor Magyar, Kolozsvár.)

The problem was also solved by: Barna D., Beck F., Brandt D., Devecis M., Erdős A., Fekete J., Freibauer E., Goldziher K., Kármán T., Orlowszky F., Schiffer H., Szabó I., Szabó K.