In a group of400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Explanation

Let H represents the set of people who can speak Hindi and E, who can speak English.
Then, `n(H) = 250 and n(E) = 200`
So, `H cup E` will be the set of people who can speak Hindi or English
`n(H cup E) = 400`
Clearly, `n(H cap E)` will be the number of people who can speak Hindi and English both
Now, `n(H cupE)=n(H)=+n(E)-n(H capE)`
`rArr 400=250+200-n(HcapE)`
`n(H cap E)= 450 - 400= 50`
Therefore, number of people who can speak Hindi and English both are 50.