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 and one person can speak all the three languages, then how many persons are there in the group ?

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.