jmc

Since there were $20$ males last year, there are $1.05\cdot 20=21$ males this year.

We set the number of females last year as $x$. This means that there are $1.2x$ females this year.

In total, there were $20+x$ people in the league last year, and $1.1\cdot (20+x)$ this year. We then have: $$\begin{array}{rl}22+1.1x& =21+1.2x\\ 1& =0.1x\\ x& =10.\end{array}$$ Therefore, there were $10$ girls last year. This means there are $1.2\cdot 10=12$ girls this year. So there are $\frac{12}{12+21}=\frac{12}{33}=\boxed{\frac{4}{11}}$ girls out of the participants this year.