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?

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?

Answer
Let H and E is the set of students who know Hindi and English respectively.
n(H) = 100, n(E) = 50 and n(H ∩ E) = 25
Use formula
n ( H ∪ E ) = n (H ) + n ( E ) – n ( H ∩ E)
Plug the values we get,
= [100 + 50 - 25]
⇒ 125
Therefore, there are 125 students in the group.