Question

The average salary of a male employees in a firm is Rs 520 and that of female employee is Rs 420 The mean salary of all the employees is Rs 500 What is the percentage of female employee?

• A. $40$%
• B. $30$%
• C. $25$%
• D. $20$%

Answer 1

Answer: (D)

$20$%

Let the number of male employees be $n_1$

and the number of females employees be $n_2$

Average salary of the male employees be $\overline{x_1}=520$

and the average salary of females employees be $\overline{x_2}=420$

Average salary of all employees $=\overline{x}$=500

Now, $\overline{x}=\frac{n_1\overline{x_1}+n_2\overline{x_2}}{n_1+n_2}$

$=>500=\frac{n_1\left(520\right)+n_2\left(420\right)}{n_1+n_2}$

$=>500n_1+500n_2=520n_1+420n_2$

$=>80n_2=20n_1$

$=>\frac{n_2}{n_1}=\frac{20}{80}$

$=\frac{n_2}{n_1}=\frac{1}{4}$

Let the number of female employees be x,

Then the number of males employees is 4x

Total employees $=5x$

Now, percentage of female employees $=\frac{x}{5x}\times 100$% $=20$%