Question

A survey was taken of 100 employees in a company. Exactly 28 of them had an MBA. The
number of women without an MBA was 12 more than the number of men with an MBA. What
fraction of the surveyed employees were men?
1) 16/25
2) 2/5
3) 3/5
4) 13/25 ​

Answer 1

Given:

No. of employees = 100

No. of employees who had an MBA = 28

To find:

The fraction of surveyed employees.

Solution:

Let $M$ be the no. of men employees who have an MBA and $M'$ be the no. of men employees who do not have an MBA.

Let $W$ be the no. of women employees who have an MBA and $W'$ be the no. of women employees who do not have an MBA.

Then, no. of employees in the company is the sum total of all men and women who have and do not have an MBA,

$M+M'+W+W'=100$

No. of employees who have an MBA,

$M+W=28$

No. of employees who do not have an MBA = No. of employees - No. of employees who have an MBA

$M'+W'=100-28$

$M'+W'=72...(1)$

It is also given that no. of women without an MBA was 12 more than the number of men with an MBA, which means,

$W'=12+M...(2)$

Substituting equation (2) in equation (1)

$M'+12+M=72$

$M'+M=72-12$

$M'+M=60$

i.e., 60 men employees have and do not have an MBA in the company which is the total no. of men employees in the company.

Fraction of the surveyed employees were men = No. of men employees/Total no. of employees

Fraction of the surveyed employees were men = $\frac{60}{100}=\frac{3}{5}$

Hence, option (3) is correct.

$\frac{3}{5}$ of the surveyed employees were men. Option (3) is correct.