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In a group of 65 people, 40 people like cricket and 10 people like both cricket and tennis. Everyone in the group likes at least one of the two games. How many people like only tennis?

In a group of 65 people, 40 people like cricket and 10 people like both cricket and tennis. Everyone in the group likes at least one of the two games. How many people like only tennis? Correct Answer 25

Given:

In a group of 65 people, 40 people like cricket and 10 people like both cricket and tennis

 Everyone in the group like at least one of the two games

Formula used:

n(C U T) = n(C) + n(T) - n(C ∩ T) 

Explanation:

Let T and C denote people who like Tennis and Cricket respectively

Total number of people = Number of people who like Cricket or Tennis

⇒ n(C U T) = 65

Number of people who like Cricket = n(C) = 40

Number of people who like both Cricket and Tennis = n(C ∩ T) = 10

Now,

n(C U T) = n(C) + n(T) - n(C ∩ T) 

⇒ n(T) = n(C U T) + n(C ∩ T) - n(C)

⇒ n(T) = 65 + 10 - 40 = 35

∴ Number of people like only tennis = 35 - 10 = 25

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