3. (7 points) In the first stage of the mathematics Olympiad, $a \%$ of the participants were girls, and among the participants of the informatics Olympiad, $b \%$ were girls. It is also known that no one participated in both subjects, and among all the participants of the first stage, $c \%$ were girls. Find the ratio of the number of girls who participated in the informatics Olympiad to the number of girls who participated in the mathematics Olympiad $(a>c>b)$.
Solution: Let $x$ be the total number of participants in the mathematics Olympiad, and $y$ be the total number of participants in the informatics Olympiad. Then

$$
c=\frac{a x+b y}{x+y} \Longrightarrow \frac{y}{x}=\frac{a-c}{c-b}
$$

The desired ratio is

$$
\frac{b y}{a x}=\frac{b(a-c)}{a(c-b)}
$$

Answers:

| Option | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Answer | 0.3 | 0.2 | 2.5 | 0.3 | 1.7 | 1.5 | 0.8 | 1.2 | 1.8 | 2.5 |