A homeowner pays a 10% income tax on the rent. By what percentage does the homeowner need to increase the rent to keep the income the same if the income tax is raised to 20%?
If the rent is $a$, and the increased rent is $x$ percent, then

$$
a-\frac{a}{10}=a+\frac{a x}{100}-\frac{\left(a+\frac{a x}{100}\right) 20}{100}
$$

or

$$
\frac{9}{10}=\frac{4}{5}\left(1+\frac{x}{100}\right)
$$

from which

$$
x=12.5 \% \text {. }
$$

(Zoltán Harsányi, Eger.)

The problem was also solved by: Ehrenstein P., Freund E., Füstös P., Gerő M., Jánossy F., Jánosy Gy., Kiss J., Paunz A., Reich Z., Sárközy E., Schlesinger Gy., Schuster Gy., Schwarz Gy., Schwarz O., Tóth B. - The Budapesti Ág. h. ev. fógymn, 5th grade.