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 H be the set of people who know Hindi and E be the set of people who know English
Then `(H cap E)` will represent the set of people who know Hindi and English both
Here `n(H) = 100,n(E) =50 and n(H cap E) = 25`
Now `n(H cup E) = n(H) +(E)- n(H cap E) =25`
`rArr n(H cup E)=100+50 -25`
`rArr n (H cup E)=125`
Therefore, total number of students in the group = 125.