The average salary of male employees in a firm was $52$ and that of female employees was $₹42$. If the mean salary of the employees was $50$, what was the percentage of female employees?

We can solve this easily using the rule of Alligation:
* Average salary of male employees ($M$) = $52$
* Average salary of female employees ($F$) = $42$
* Mean salary of all employees ($G$) = $50$

By Alligation:

$$\text{Ratio of Male to Female}=\frac{G-F}{M-G}=\frac{50-42}{52-50}=\frac{8}{2}=\frac{4}{1}$$

So, the ratio of Male $:$ Female employees is $4:1$.

Now, calculate the percentage of female employees:

$$\text{Percentage of female employees}=\frac{1}{4+1}\times 100\%=\frac{1}{5}\times 100\%=20\%$$