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?

Solution:

Let U be the set of all students in the group.

E be the set of all students who know English.

H be the set of all students who know Hindi.

It is given that

n (H) = 100, n (E) = 50, n (H ∩ E) = 25

We know that

n (H υ E) = n (H) + n (E) - n (H ∩ E)

= 100 + 50 - 25

= 150 - 25

= 125

Hence, there are 125 students in the group.

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 14

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?

Summary:

In a group of students 100 students know Hindi, 50 know English and 25 know both are given. We have found that there are 125 students in the group