Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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A Survey Shows that 76% of the Indians like Oranges, Whereas 62% like Bananas. What Percentage of the Indians like Both Oranges and Bananas? - Mathematics

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

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Solution

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

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

Concept: Universal Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.8 | Q 6 | Page 47
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