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

Find Percentage of Indians Who Like Both Orange and Bananas

Question:

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

Solution

\[ n(O\cup B)=n(O)+n(B)-n(O\cap B) \]

Since every Indian likes at least one of the two fruits,

\[ 100=76+62-n(O\cap B) \] \[ 100=138-n(O\cap B) \] \[ n(O\cap B)=138-100 \] \[ n(O\cap B)=38 \]

Hence, 38% Indians like both orange and bananas.

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