Fedorov R.M.

In the Banana Republic, parliamentary elections were held in which all residents participated. All those who voted for the "Mandarin" party love mandarins. Among those who voted for other parties, 90% do not like mandarins. What percentage of the votes did the "Mandarin" party receive in the elections, if exactly $46\%$ of the residents love mandarins?
Find in two ways how many people love tangerines.

## Solution

Let the entire population of the republic be $-N$ people, of which $M$ people voted for "Tangerine." Then, on one hand, tangerines are loved by $0.46 N$ people, and on the other hand, this number is equal to the number of people who voted for "Tangerine" plus $10\%$ of the remaining, that is, $0.1(N-M)$. Therefore, $M+0.1(N-M)=0.46 N$, or $0.9 M=0.36 N$. Thus, ${ }^{M} / N=$ $0.36: 0.9=0.4$.

## Answer

$40 \%$.