I am part of a Math Club, where I have the same number of male colleagues as female colleagues. When a boy is absent, three quarters of the team are girls. Am I a man or a woman? How many women and how many men are there in the club?
Let $H$ and $M$ be the numbers of men and women, respectively, in the club. We have two possibilities. If I am a boy, then $M=H-1$ and, when one boy is missing, the total number of people in the club is

$$
M+H-1=H-1+H-1=2 H-2
$$

Thus, $H-1=M=\frac{3}{4}(2 H-2)$, which implies $H=1$. But then, $M=1-1=0$, which is not possible. Therefore, I must be a girl, and thus $M=H+1$ and we have $H+1=\frac{3}{4}(2 H+1-1)$, from which $H=2$ and $M=3$.