#### 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?

#### Solution

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

Accordingly, *n*(H) = 100 and *n*(E) = 50

n(H∩E) = 25

*n*(U) = *n(*H) + n(E) – *n*(H ∩ E)

*= *100 + 50 – 25

*=* 125

Hence, there are 125 students in the group.

Is there an error in this question or solution?

Solution 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? Concept: Practical Problems on Union and Intersection of Two Sets.