Question

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 1

Let A and B be the numbers of students who know Hindi and English respectively.

Therefore, n( A )=100

n( B )=50

n( A∩​B )=25

Since each student knows either Hindi or English,

( A∪B )=Total number of students

( A∪B )=n( A )+n( B )−n( A∩B ) =100+50−25 =125

Thus, the total number of students in the group is 125 .