In a survey it is to be found that 70% of employees like bananas and 64% like apples. If x% like both bananas and apples, then

Question

In a survey it is to be found that 70% of employees like bananas and 64% like apples. If $x$ % like both bananas and apples, then

Smart Achievers · Accepted Answer

(3)

$Let A and B denote the set of employees who like$ $bananas and apples respectively and total number of employees be 100 .$

$∴$ $n (A) = 70, n (B) = 64, n (U) = 100 and n (A \cap B) = x$

$Now, n (A \cup B) \leq 100$

$∴$ $n (A) + n (B) - n (A \cap B) \leq 100$

$\Rightarrow$ $70 + 64 - x \leq 100 \Rightarrow x \geq 34$ ...(i)

$Also, A \cap B \subseteq B$

$∴$ $n (A \cap B) \leq n (B) \Rightarrow x \leq 64$ ...(ii)

$By (i) and (ii), we have 34 \leq x \leq 64$

Want Us to Email you About Special Offers & Updates?