In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali only? How many can speak both Hindi and Bengali?

Explanation

Let H and B be the set of those people who can speak Hindi and Bengali respectively, then according to the problem, we have
`n(HuuB) = 1000`,
n(H) = 750, n(B) = 400
We know that,
`n(HuuB)=n(H)+n(B)-n(HnnB)`
`1000=750+400-n(HnnB)`
`therefore n(HnnB)=150`
`therefore` Number of people speaking Hindi and Bengali both is 150.
Also, `n(HnnB')=n(H)-n(HnnB)`
= 750-150
= 600
Thus, number of people speaking Hindi only is 600.
Again, `n(BnnH')=n(B)-n(BnnH)=400-150=250`
Thus, number of people speaking Bengali only is 250.