In a group of persons traveling 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 ?
Answers
The Correct answer is.....
21 Persons
Explanation:
There are 21 persons in that group.
Let us find solutions...
Given...
6 persons can speak Tamil
15 persons can speak Hindi
6 persons can speak Gujarati
and
2 persons can speak two languages. (It can be Hindi-Tamil, Hindi-Gujarati or Gujarati-Tamil)
1 person can speak all three languages.
The number of persons who can speak Tamil is 6.
So only Tamil speaking persons are 6 – 2 – 1 = 3
The number of persons who can speak Hindi is 15.
So only Hindi speaking persons are 15 – 2 – 1 = 12
The number of persons who can speak Gujarati is 6.
So only Gujarati speaking persons are 6 – 2 – 1 = 3
Thus the number of persons who can speak only one language is 3 + 12 + 3 = 18
The Number of persons who can speak two languages = 2
The Number of persons who can speak all three languages = 1
The total number of persons is = 18 + 2 + 1 = 21
So there are 21 persons in the group
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