In a group of 500 people, 350 speak Hindi and 300 speak English. It is given that each person speaks at least one language.
(i) How many people can speak both Hindi and English?
(ii) How many people can speak Hindi only?
(iii) How many people can speak English only?

Explanation

Let H be the set of people who speak Hind, and E be the set of people who speak English.
`therefore n(H cup E)= 500 ,n(H)= 350,n(E)=300`
We have to find `n(H cap E)`.
Now `n (H cup E)=n(H)+n(E)-n(H cap )`
`therefore 500=350 + 300 -n (H cap E)`
`rArr 500=650 -n (H cap E)`
`therefore n(H cap E )=150`
Thus, 150 people can speak both Hindi and English. Number of people who speak Hindi only `= n(H) - n(H cap E) `
= 350 150 = 200 Number of people who speak English only `= n(E) n(H cap E)`
= 300 - 150 =150