Question

A survey shows that $63\%$ of the Americans like cheese where as $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples, then the value of $x$ is

• A. $39 \leq x \leq 63 $
• B. $63$
• C. $39$
• D. $139 \geq x$

Answer 1

Answer: (A)

Let total Americans be 100
$\therefore$ Let A Americans like cheese
$\therefore$ Let B Americans likes apple.
$ \therefore n ( A )=63, n ( B )=76 $
Then $n(A \cup B)=100$
$ \begin{array}{l} \therefore n ( A \cap B )= n ( A )+ n ( B )- n ( A \cup B ) \\ \Rightarrow n =63+76-100 \\ \Rightarrow n =39 \end{array} $