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In a company the average salary of male employees is Rs. $9200$ and that of female employees is Rs. $8200$. If the average salary per employee is Rs. $8900$, the percentage of female employee of the total employee is A) $30$B) $40$C) $50$D) $25$

Last updated date: 20th Jun 2024
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Hint: At first, we find the total salary of female employees. Then the total salary of male employees.
Next, we will find the total salary of all the employees.
Equating the salaries we can find the number of female employees.

It is given that; the average salary of male employees is Rs. $9200$
The average salary of female employees is Rs. $8200$.
The average salary per employee is Rs. $8900$.
We have to find the number of female employees.
Let us take the total number of employees to be $100$.
The number of female employees is $x$. So, the number of male employees is $100 - x$.
The total salary of $x$ numbers of female employees is $8200x$.
Total salary of $x$ numbers of male employees is $9200(100 - x)$.
Total salary of $100$ numbers of employees is $8900 \times 100$.
According to the problem we get,
$\Rightarrow 9200(100 - x) + 8200x = 8900 \times 100$
Simplifying we get,
$\Rightarrow 920000 - 9200x + 8200x = 890000$
Simplifying again we get,
$\Rightarrow 1000x = 30000$
Solving we get,
$\Rightarrow x = 30$

$\therefore$ The number of female employees is $30$. Hence, the correct answer is option (A).

Note:
An average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list.
The average is defined as the mean value which is equal to the ratio of sum of number of given set of values to the total number of values present in the set.
We know that the value of percentage means 100.