A homeowner pays $\frac{1}{11}$ of their total rental income in taxes. By what percentage must they increase the rent so that their net income does not change if the tax rate is raised to $\frac{1}{10}$ of their total income?
If a landlord increases the rent by $x$ percent, then his total income is $N+\frac{N x}{100}$, where $N$ represents the previous total income. According to the problem,

$$
N-\frac{N}{11}=N+\frac{N x}{100}-\left(N+\frac{N x}{100}\right) \frac{1}{10}
$$

from which

$$
x=1 \frac{1}{99} \%
$$

(Zoltán Jármay, Budapest.)