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 and every person speaks at least one language. If 2 persons in the group speak exactly two languages and one person speaks exactly all the three languages, then how many persons are there in the group?
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 and every person speaks at least one language. If 2 persons in the group speak exactly two languages and one person speaks exactly all the three languages, then how many persons are there in the group?
The correct option is
C
23
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 can speak all the languages = 1
Total number of persons = 23.
The correct option is
C
23
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 can speak all the languages = 1
Total number of persons = 23.
