# A survey shows that

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 :

1. (1) 29

2. (2) 37

3. (3) 65

4. (4) 55

Correct Option: , 4

Solution:

Let $n(U)=100$, then $n(A)=63, n(B)=76$

$n(A \cap B)=x$

Now, $n(A \cup B)=n(A)+n(B)-n(A \cap B) \leq 100$

$=63+76-x \leq 100$

$\Rightarrow x \geq 139-100 \Rightarrow x \geq 39$

$\because n(A \cap B) \leq n(A)$

$\Rightarrow x \leq 63$

$\therefore 39 \leq x \leq 63$