1)

In a survey conducted among 100 families, it is known that 77 families use LPG and 65 families use coal for cooking.

If each of the families uses at least one between LPG and  coal, how many families use both of them?


A) 31

B) 42

C) 30

D) 35

Answer:

Option B

Explanation:

The fact each of the families uses at least one implies that none equals zero.

Venn Diagram

From diagram we get

(77-x)+x+(65-x)=100

$\Rightarrow 142-x=100$

$\Rightarrow x=42$