Question

A group of people like - Khus, Mango, or Orange. $60$ like Khus, $50$ like Orange, $48$ like Mango. $12$ like Khus and Mango, $15$ like Mango and Orange, and $20$ like Orange and Khus. What are the minimum and the maximum number of people in the group respectively?

• A. 115, 119
• B. 111, 123
• C. 123, 135
• D. 111, 121

Answer 1

The correct option is B 111, 123


Let the $x$ be the number of people, who likes all three items Khus, Mango and Orange.
then possibility of $x$ would be:
Minimum $x=0$ as may none of them like three items and
Maximum $x=12$ as from the figure $12$ is the minimum number of people, who likes any two items
From , the figure the total number of people $=(x+28)+(x+15)+(x+21)+(20-x)+(12-x)+(15-x)+x=111+x$
Hence, Minimum Total $=111+0=111$
Maximum Total $=111+12=123$