In a group of 70

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.