In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Solution:

Let C denote the set of people who like cricket, and T denote the set of people who like tennis.

It is given that in a group of 65 people, 40 like cricket, 10 like both cricket and tennis.

Therefore,

n (C) = 40, n (C υ T) = 65 and n (C ∩ T) = 10

Finding the number of people who like tennis:

We know that n(C υ T) is,

n (C υ T) = n (C) + n (T ) - n (C ∩ T)

From this,

n (T) = n (C υ T) + n (C ∩ T) - n (C)

= 65 + 10 - 40

= 75 - 40

= 35

Hence, number of people who like tennis, n (T) = 35

Finding the number of people who like tennis only and not cricket:

the number of people like tennis only and not cricket = n (T - C).

As we know

n (T) = n (T - C) + n (C ∩ T)

n (T - C) = n (T) - n (C ∩ T)

= 35 - 10

= 25

Therefore, 35 people like tennis and 25 people like tennis only and not cricket.

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NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 7

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Summary:

It is given that a group of 65 people, 40 like cricket, 10 like both cricket and tennis. We have found that 25 people like tennis only and not cricket; and 35 people like tennis.