In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Here, Number of students who know Hindi,`n(A) = 100`

Number of students who know English,`n(A) = 50`

Number of students who know both languages,`n(AnnB) = 25`

As each of the students knows either Hindi or English, total number of students will be `n(AuuB)`.

We know,`n(AuuB) = n(A)+n(B)-n(AnnB) = 100+50-25 = 125

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Let H = set of students, who know Hindi

E = set of students, who know English

Then n(H) = 100; n(E) = 50 and n(H∩E) = 25.

∴ n(H∪E) = n(H) + n(E)-n(H∩E)

= 100 + 50 – 25 = 125

Hence, 125 students are there in the group.