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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?
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?
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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