Solution: Let $n_m$, $n_f$ denote the number of male and female employees in the firm respectively. Further assume that \begin{align*} x_m & = \text{ the average salary of male employees } \\ x_f & = \text{ the average salary of female employees } \\ x & = \text{ average salary of all the employees } . \end{align*} According to the problem, \begin{align*} x_m = 520 \quad x_w = 420 \quad \text{ and } \quad x = 500. \end{align*} We have \begin{align*} x = \frac{n_m x_m + n_f x_f}{n_m + n_f} & \implies 500 = \frac{520 n_m + 420 n_f}{n_m + n_f}\\ & \implies 500(n_m + n_f) = 520 n_m + 420 n_f\\ & \implies 20 n_m - 80 n_f = 0 \\ & \implies \frac{n_m}{n_f} = \frac{4}{1}. \end{align*} Therefore, the percentage of male employees in the firm will be \[ \frac{4}{4 + 1} \times 100 = 80\% \] and the percentage of male employees in the firm will be \[ \frac{1}{4 + 1} \times 100 = 20\%. \]