Question:
A survey shows that $63 \%$ of the people in a city read newspaper $A$ whereas $76 \%$ read newspaper $B$. If $x \%$ of the people read both the newspapers, then a possible value of $x$ can be :
Correct Option: , 4
Solution:
Let $n(U)=100$, then $n(A)=63, n(B)=76$
$n(A \cap B)=x$
Now, $n(A \cup B)=n(A)+n(B)-n(A \cap B) \leq 100$
$=63+76-x \leq 100$
$\Rightarrow x \geq 139-100 \Rightarrow x \geq 39$
$\because n(A \cap B) \leq n(A)$
$\Rightarrow x \leq 63$
$\therefore 39 \leq x \leq 63$
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