In a group of persons travelling in a bus, 6 persons can speak Tamil
In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages only and one person can speak all the three languages, then how many persons are there in the group?
- 21
- 22
- 23
- 24
Answer
n(T) = 6; n(H) = 15; n(G) = 6
n(T ∩ H ∩ G) = 1
n(T ∩ H) = n(H ∩ G) = n(T ∩ G) = 2
n(T U H U G) = n(T) + n(H) + n(G) - n(T ∩ H) - n(H ∩ G) - n(T ∩ G) + n(T ∩ H ∩ G)
= 6 + 15 + 6 - 2 - 2 - 2 + 1 = 22
The correct option is B.