Someone buys two estates; one yields 1560 francs, the other, which was 7000 francs cheaper and yields \(\frac{1}{2} \%\) less, brings in 515 francs less annually; how much did the two estates cost and what percentage do they yield?
If one of the estates was sold for $x$ forints and yielded $y$ percent profit, then according to the problem:

$$
\begin{gathered}
\frac{x y}{100}=1560 \\
\frac{(x-7000)\left(y-\frac{1}{2}\right)}{100}=1560-515
\end{gathered}
$$

From this equation, $x_{1}=26000, y_{1}=6$ and $x_{2}=84000, y_{2}=1 \frac{6}{7}$. Both solutions are valid for the problem. One estate was sold for 26000 or 84000 forints and yielded a profit of 6 or $1 \frac{6}{7}$ percent, while the other was sold for 19000 or 77000 forints and yielded a profit of $5 \frac{1}{2}$ or $1 \frac{5}{14}$ percent.

(Szibelth Sándor, Székesfehérvár.)

The problem was also solved by: Barabás S., Dolowschiák M., Filkorn J., Juvancz I., Kárf J., Kohn B., Kürth A., Lukhaub Gy., Mandel M., Petrogalli G., Spitzer Ö., Weisz J.