Question

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 like both coffee and tea?

Answer 1

A total number of people = 70. 

Number of people liking Coffee = n(C) = 37. 

Number of people liking Tea = n(T) = 52 

Total number = n (C ∪ T) = 70 

Person who likes both would be n(C ∩ T) 

We know, 

n (C ∪ T) = n(C) + n(T) – n (C ∩ T) 

Substituting the values we get 

70 = 37+52– n (C ∩ T) 

70 = 89 – n (C ∩ T) 

n (C ∩ T) =19. 

∴ There are 19 persons who like both coffee and tea.