Sets-Relations-And-Functions Question 148

Question: There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:

Options:

A) 100

B) 200

C) 300

D) 400

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a]Let $ A\equiv $ Set off Tamil speaking students and $ B\equiv $ Hindi speaking students $ n(A)=400,n(B)=300 $ and $ n(A\cup B)=600 $ $ n(A\cup B)=n(A)+n(B)-n(A\cap B) $

$ \Rightarrow n(A\cap B)=n(A)+n(B)-n(A\cup B) $ $ =400+300-600=100 $