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 language 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

The correct option is C $23$

People can speak tamil, hindi and gujrati

Tamil speakers – persons who can speak is $6$.

Only Tamil speakers are $6–2–1=3$

Hindi speakers - persons who can speak is $15$.

Only Hindi speakers are $15–2–112$

Gujarati speakers – persons who can speak is $6$.

Only Gujarati speakers are $6–1=5$

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 = $23$.

Hence, Option $C$ is correct.