Question

In a group of 80 employees, the number of employees who are engineers is twice that of the employees who are MBA. The number of employees who are not engineers is 32 and employees who are both engineers and MBA is twice that of the employees who are only MBA. How many employees are neither engineer nor MBA?

• A. 24
• B. 38
• C. 36
• D. Cannot be determined

Answer 1

The correct option is A 24

Let a be the number of engineers only

c be the number of MBA only
b be the number of emplotees who are both engineers and MBA and
d be the number of employees who are neither engineer nor MBA
$\therefore$ a + b + c + d = 80 . . . (1)
(a + b) = 2(b + c) $\Rightarrow$ (a - b) = 2c . . . (2)
and c + d = 32 . . . (3)
and a + d = 56 . . . (4)
and b = 2c . . . (5)
From eqs (2) and (5), we get
a = 2b
From eqs (1) and (3), we get
a + b = 48 . . . (6)
From eq. (6) we get
b = 16
$\therefore$ a = 32 (from eq. 6)
and c = 8 (from eq. 5)
and d = 24



Hence, 24 employees are neither engineer nor MBA.