A survey show 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

Suppose that there are 100 people are there in the city

Given $n (A) = 63, n (B) = 76, n (A \cap B) = x$

The addition theorem on cardinal number of sets

$n (A \cup B) = n (A) + n (B) - n (A \cap B)$

Substitute the apropriate values

we get

$\begin{array}{rcl} n (A \cup B) & = & n (A) + n (B) - n (A \cap B) \\ = & 63 + 76 - x \\ = & 139 - x \end{array}$

$A \subseteq A \cup B, B \subseteq A \cup B \Rightarrow n (A) \leq n (A \cup B), n (B) \leq n (A \cup B)$

Therefore,

$\begin{array}{rcl} 76 & \leq & 139 - x \leq 100 \\ - 63 & \leq & - x \leq - 39 \\ 39 \leq x \leq 63 \end{array}$

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