Gabi bought two rare singing birds. Later, he sold them, both for the same price. This way, he lost 20% on one, but gained 20% on the other, yet overall he still lost 10 Ft. For how much did he buy and sell the birds?
The loss of 20% (price reduction) on the more expensive bird is $10 \mathrm{Ft}$ greater than the 20% profit (price increase) on the other. Due to the equality of the ratios, the final $10 \mathrm{Ft}$ loss is also 20% of the difference in the purchase prices, which was $50 \mathrm{Ft}$. The equality of the selling prices eliminated this difference, so the total change is also $50 \mathrm{Ft}$. If we divide this into two parts, whose difference is $10 \mathrm{Ft}$, we get the 20-20% of the purchase prices. These two parts are $30 \mathrm{Ft}$ and $20 \mathrm{Ft}$, so the two purchase prices are $150 \mathrm{Ft}$ and $100 \mathrm{Ft}$, and the common selling price is $120 \mathrm{Ft}$.

Horváth Magda (Nagykanizsa, Landler J. g. I. o. t.)

Note. Many solutions unnecessarily used equations, or even systems of equations to solve the problem. A solution using simpler tools is more interesting.