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?

Answer 1

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.

JAI SHREE KRISHNA