In a group of 1000 people all of whom speak atleast one of Bengali or Hindi language, there are 750 who can speak Hindi and 400 who can speak Bengali. If number of people who can speak Bengali only is B and the people who can speak both Hindi and Bengali is C, then.

Explanation

Let H and B denote the sets of those people who can speak Hindi and Bengali respectively.

Given
`n(HuuB)=1000,n(H)=750,n(B)=400`.

Now
`n(HuuB)=n(H)+n(B)−n(HnnB)`

`1000=750+400−n(HnnB)`

`⇒(HnnB)=150.`

Hence `150 `people can speak both Hindi and Bengali.


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