Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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?

#### 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