In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujrati. 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 thee three languages, then how many persons are there in the group?

Using inclusion-exclusion with overlaps: Let T = Tamil only, H = Hindi only, G = Gujarati only. Two-language speakers = 2, Three-language speaker = 1. Total Tamil speakers = T + (overlaps) = 6. Total Hindi = H + (overlaps) = 15. Total Gujarati = G + (overlaps) = 6. The overlaps involve the multilingual speakers. Working through systematically: Total = 6 (Tamil) + 15 (Hindi) + 6 (Gujarati) - 2 (counted twice) - 2×1 (counted thrice) = 23. Alternative approach: Count unique persons by carefully accounting for multilingual speakers.