    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: $37$$29$$65$$55$

A

$37$

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B

$29$

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C

$65$

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D

$55$

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Solution

## The correct option is D$55$ Finding the value of x:Let the people read news $A$is $n\left(A\right)=63%$the people read news $B$is $n\left(B\right)=76%$the people read both the newspapers $n\left(A\cap B\right)=x$We know that $max\left(n\left(A\right)&n\left(B\right)\right)\le n\left(A\cup B\right)\le 100$$⇒$$76\le 63+76-x\le 100$$⇒$$-63\le -x\le -39$$⇒$ $63\ge x\ge 39$Hence, correct answer is option $\left(D\right)$.  Suggest Corrections  36      Similar questions  Explore more