Three numbers are in the ratio of $2: 3: 4$. The sum of the squares of these numbers is 725. What are these numbers?
Let these be three numbers: $2 x, 3 x, 4 x$; then, according to the problem:

$$
29 x^{2}=725
$$

from which

$$
x= \pm 5
$$

The sought numbers are thus: $10,15,20 ;$ or : $-10,-15,-20$.

The problem was solved by: Bálint Béla, Berger Hugo, Feuer Mór, Freund Antal, Friedmann Bernát, Geist Emil, Goldschmiedt Áron, Goldstein Zsigmond, Goldziher Károly, Grünhut Béla, Hofbauer Ervin, Kántor Nándor, Klein Mór, Kornis Ödön, Pivvarcsy Jenő, Porde Gyula, Riesz Frigyes, Schneider Béla, Simon Elek, Szabó István, Weisz Ármin.