In a group of 70 people 37 like coffee 52 like tea and each person likes at least one of the two dri...........

Logical Reasoning(Master ) Logical Venn Diagrams

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. The number of persons liking both coffee and tea is

none of these

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Explanation:

Let C and T represent the set of people who like coffee and tea respectively.
Number of person likes at least one of the two drinks, n(C ∪ T) = 70
Number of person like coffee, n(C) = 37
Number of person likes tea, n(T) = 52
Use the formula
n(C ∪ T) = n(C) + n(T) - n(C ∩ T)
Plug the values, we get
70 = 37 + 52 - n(C ∩ T)
⇒ 70 = 89 - n(C ∩ T)
⇒ n(C ∩ T) = 89 - 70 = 19

Hence, option 1 is the correct answer.