Question

A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?

Answer 1

Let us denote the people who like oranges by n(O) = 76 

Let us denote the people who like oranges by n(B) = 62 

Total number of people will be those who like oranges or banana = n (O∪ B) =100 

People who like both oranges and banana = n (O ∩ B) 

We know, 

n (O ∪ B) = n(O) + n(B) – n (O ∩ B) 

Substituting the values we get 

100 = 76+62 – n (O ∩ B) 

100 = 138 – n (O ∩ B) 

n (O ∩ B) = 38 

People who like both oranges and banana = 38%.