question_answer

In a group of 1000 people, 700 can speak English and 500 can speak Hindi. If all the people speak atleast one of the two languages, then find how many can speak both the languages?

A) 200

B) 300

C) 400

D) 500

Correct Answer: A

Solution :

[a] \[\because \]\[n\,(E\cup H)=n\,(E)+n\,(H)-n\,(E\cap H)\]             \[\Rightarrow \]\[100=700+500-n\,(E\cap H)\]           \[\left[ \begin{align}   & E\to English \\  & H\to Hindi \\ \end{align} \right]\]             \[\Rightarrow \]\[n\,(E\cap H)=200\]