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? 

(a) 21 (b) 22 (c) 23 (d) 24

Answer 1

(c) Let a = Speaks one language

Let b = Speaks two language

Let c = Speaks three language then

a + 2b + 3c = 6 +15 +6

a + 4 + 3 = 27

a = 20

 ∴ Total number of persons in the group

= 20 + 2 + 1 = 23.