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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?

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Let U be the set of all students in the group.
Let E be the set of all students who know English.
Let H be the set of all students who know Hindi.
∴H∪E=U
Given n(H)=100 and n(E)=50
n(H∩E)=25
n(U)=n(H)+n(E)−n(H∩E)
=100+50−25
Hence, there are 125 students in the group.
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