A survey shows that 63 % of the people in a city read newspaper A...

$n\left(A\right) = 63$

$n\left(B\right) = 76$

$n\left(A \cap B\right) = x$

Let $n\left(\cup \right) = 100$

$n\left(A \cup B\right) = n\left(A\right) + n\left(B\right) - n\left(A \cap B\right) \le 100$

$⇒ 63 + 76 - x \le 100$

$⇒ x \ge 39$

But $n\left(A \cap B\right) \le n\left(A\right)$

$∴ 39 \le x \le 63$ .