Question

The average salary of male employees in a firm was Rs5200 and that of females was Rs4200. The average salary of all the employees was Rs5000. What is the percentage of female employees?
A) \[80\% \]
B) \[20\% \]
C) \[40\% \]
D) \[30\% \]

Answer 1

Hint:
Here, we have to form an equation from the data given in the question and by solving the equation we will get the ratio of the total number of male employees to the number of the female employees. Then with the help of the ratio we will be able to get the percentage of female employees in the firm.

Complete step by step solution:
Let M be the number of male employees and F be the number of female employees.
Therefore, total employees in the firm is \[{\text{M + F}}\]
It is given that Rs5200 is the average salary of male employees and Rs4200 is the average salary of female employees
Therefore, the total salary of all the employees \[{\rm{ = Rs(5200M + 4200F)}}\]………. (1)
Also it is given that the average salary of all the employees is Rs5000.
Therefore, total salary of all the employees \[{\rm{ = Rs(5000(M + F)) = Rs(5000M + 5000F)}}\] ………. (2)
Now we will equate the equation (1) and (2), we get
\[{\rm{5200M + 4200F}} = {\rm{5000M + 5000F}}\]
\[ \Rightarrow {\rm{200M = 800F}}\]
\[ \Rightarrow \dfrac{{\rm{M}}}{{\rm{F}}} = \dfrac{{800}}{{200}} = \dfrac{4}{1}\]
So, from the above ratio of total number of male employees to the number of the female employees we will be able to find the percentage of female employees in the firm
Therefore, percentage of female employees in the firm \[{\rm{ = }}\dfrac{{{\text{Number of female employees}}}}{{{\text{Total employees}}}} \times 100\% \]
Percentage of female employees in the firm \[ = \dfrac{1}{5} \times 100\% = 20\% \]

Hence, there are only \[20\% \] female employees in the firm.
So, option B is correct.

Note:
Average of some numbers is equal to the ratio of the sum of the numbers to how many numbers are being added. Concept of percentage is generally used for analysis purposes as it makes the numbers easy to read. It is generally used in almost every report. Percentage makes the analysis easy and also helps a lot in prediction of the future data. It helps mostly for the data with the big numbers in it like we used in the above example.