In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Solution:

Let C denote the set of people who like coffee, and T denote the set of people who like tea.

It is given that in a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks.

Therefore,

n (C) = 37, n (T) = 52 and n (C υ T) = 70.

We know that n(C υ T) is given by,

n (C υ T) = n (C) + n (T) - n (C ∩ T)

From this,

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

= 37 + 52 - 70

= 89 - 70

= 19

Therefore, 19 people like both coffee and tea.

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NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 6

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Solution:

It is given that a in group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. We have found that 19 people like both coffee and tea.