Question

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 1

Answer:

♣ The correct option is B.

Explanation:

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

Answer 2

ANSWER:-

C) 23

Explanation:

Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages.

Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3

Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12

Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5

Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20

Number of persons who can speak two languages = 2

Number of person who an speak all the languages = 1

Total number of persons = 23.