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 A & B denote the sets of the Indians who like oranges & bananas, respectively.

$$\begin{gathered} \mathrm{Given}: \\ n\left(A\right)=76\% \\ n\left(B\right)=62\% \\ n\left(A\cup B\right)=100\% \\ n\left(A\cap B\right)=? \\ \mathrm{We}\mathrm{know}: \\ n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ \Rightarrow 100=76+62-n\left(A\cap B\right) \\ \Rightarrow n\left(A\cap B\right)=38 \\ \mathrm{Therefore},38\%\mathrm{of}\mathrm{the}\mathrm{Indians}\mathrm{like}\mathrm{both}\mathrm{oranges}\&\mathrm{bananas}. \end{gathered}$$