Question

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

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Solution

The correct option is **B** 24

Let a be the number of engineers only

c be the number of MBAs only

b be the number of emplotees who are both engineers and MBAs and

d be the number of employees who are neither engineer nor MBA

∴ a + b + c + d = 80 . . . (1)

(a + b) = 2(b + c) ⇒ (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

∴ a = 32 (from eq. 6)

and c = 8 (from eq. 5)

and d = 24

Hence 24 employees are neither engineer nor MBAs.

Let a be the number of engineers only

c be the number of MBAs only

b be the number of emplotees who are both engineers and MBAs and

d be the number of employees who are neither engineer nor MBA

∴ a + b + c + d = 80 . . . (1)

(a + b) = 2(b + c) ⇒ (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

∴ a = 32 (from eq. 6)

and c = 8 (from eq. 5)

and d = 24

Hence 24 employees are neither engineer nor MBAs.

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