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 ?

Options

A. 21
B. 22
C. 23
D. 24

Answer

C

Explanation

Let circles T, H and G represent persons who can speak Tamil, Hindi and Gujarati respectively.

According to the question
Number of persons who can speak Tamil
`= a + b + d + e = 6 ..(i)`
Number of persons who can speak Hindi
`= b + c + e + f = 15 .....(ii)`
Number of persons who can speak Gujarati
`= d+e+f+g = 6..(iii)`
Number of persons who can speak any two languages
`=b + d + f = 2 ... (iv) `
Number of persons who can speak all the three languages = `e = 1 ... (v)`
Putting e = 1 in (i), (ii) and (iii), we get
`a + b + d = 5 ... (vi) `
`b + c + f = 14... (vii) `
`d + f + g = 5... (viii) `
Subtracting (iv) from (vi), we get
`a - f = 3 `
Adding (vii) and (viii), we get
`b + c + d + 2f + g = 19 ... (x)`
Adding (ix) and (x), we get
`a + b + c + d + f + g = 22 ... (x Si) `
Adding (v) and (xi), we get
`a + b + c + d + e + f + g = 23`.
Therefore, required total number of persons in the group = 23.