The average salary of male employees in a firm was Rs.520 and that of females was Rs.420. The mean salary of all the employees was Rs.500. The percentage of male employees is

Solution:

Since,${\overline{\mathrm{x}}}_1=520,{\overline{\mathrm{x}}}_2=420\text{ and }\overline{\mathrm{x}}=500$

Also we know $\overline{\mathrm{x}}=\frac{{\mathrm{n}}_1{\overline{\mathrm{x}}}_1+{\mathrm{n}}_2{\overline{\mathrm{x}}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}$

$\begin{array}{l}\Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}500\left({\mathrm{n}}_1+{\mathrm{n}}_2\right)=520{\mathrm{n}}_1+420{\mathrm{n}}_2\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}20{\mathrm{n}}_1={80}_{{\mathrm{n}}_2}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{n}}_1:{\mathrm{n}}_2=4:1\end{array}$

Hence, the percentage of male employees in the firm

$=\left(\frac{4}{4+1}\right)\times 100=80\mathrm{\%}$