You do fix the number of people, but you don't use a number, you use a letter. That way you know that your argument works no matter what number you could've chosen. Let $n$ signify the number of people before couples leave.
So, $m$ couples leaving means $2m$ people leaving, and this is $20\% = \frac15$ of the total number of people. Thus
$$
2m =\frac15n\\
$$
which is to say $n = 10m$. This second version is what we'll use later. (I didn't know from the start that I needed this second version. I added this line here after I realized way further down that the second version was what I actually needed.)
Also, we need a letter to signify the number of men before couples leaving. Let's use $k$, because $m$ is taken already. $m$ couples leaving means $m$ men leaving (assuming each couple is one man and one woman), and this is $12.5\% = \frac18$ of the total number of men:
$$
m = \frac18k
$$
Finally, the number of women before couples leave is $n-k$, since it is a standard assumption in math problems that everyone who is not a man is a woman.
So, we are asked to compare $n-k$ with $\frac13k$. We do this using the two equations we found earlier. First,
$$
n-k = 10m - k
$$
from the first equation. Then the second equation tells us that
$$
10m-k = 10\left(\frac18k\right) - k\\
= \frac{10}8k - k = \frac28k = \frac14k
$$
So the number of women before the couples leave is equal to $\frac14k$, while a third of the number of men before the couples leaving is $\frac13k$. Now it is easy to see which is larger.
