IAS 2016 — CSAT Maths

Correct Option (B)

Let M represent the number of male employees and F represent the number of female employees.

• The overall average salary for all employees is Rs 5000.
• The average salary for male employees is Rs 5200.
• The average salary for female employees is Rs 4200.

The total salary paid by the company can be expressed by equating the sum of salaries for male and female employees to the total average salary multiplied by the total number of employees:

5200M + 4200F = 5000(M + F)

Expanding the equation:

5200M + 4200F = 5000M + 5000F

Rearranging the terms to group M and F:

5200M - 5000M = 5000F - 4200F

200M = 800F

Dividing both sides by 200 yields the relationship between M and F:

M = 4F

This indicates that the number of male employees is four times the number of female employees.

To determine the percentage of male employees in the company, the following formula is used:

Percentage of Males = $\frac{\text{Number of Male Employees}}{\text{Total Number of Employees}} \times 100$Total Number of EmployeesNumber of Male Employees​×100

Percentage of Males = $\frac{M}{M+F} \times 100$M+FM​×100

Substituting M = 4F into the percentage calculation:

Percentage of Males = $\frac{4F}{4F+F} \times 100 = \frac{4F}{5F} \times 100$4F+F4F​×100=5F4F​×100

Percentage of Males = $\frac{4}{5} \times 100 = 80\%$54​×100=80%

Incorrect Options:

Options A (75%), C (85%), and D (90%) are inconsistent with the derived ratio of male to female employees and the overall average salary provided in the question. The calculated percentage of male employees is precisely 80%.