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?

Question

Philoid · Accepted Answer

Let T be the set of people who like Tea,

and C be the set of people who like Coffee.

Number of people who like Tea = n(T) = 52

Number of people who like Coffee = n(C) = 37

Number of people who like at least tea or Coffee = n(T ∪ C ) = 70

Number of people who like both tea and Coffee = n(T ∩ C )

We know that-

n(T ∪ C) = n(T)+ n(C) - n(T ∩ C)

⇒ 70 = 52+37 - n(T ∩ C)

⇒ 70 = 89 - n(H ∩ E)

⇒ n(H ∩ E) = 89-70

∴ n(H ∩ E) = 19

Thus, 19 people like both Tea and Coffee.