Question

A town has total population $25000$, out of which $13000$ read ‘The Hindustan Times and $10500$ read ‘The Indian Express’ and $2500$ read both papers. The percentage of population who read neither of these newspapers is

• A. $10\%$
• B. $16\%$
• C. $27\%$
• D. $30\%$

Answer 1

Answer: (B)

Let $X$, $A$ and $B$ be the sets of all persons, persons reading ‘The Hindustan Times’ and persons reading ‘The Indian Express’ respectively.
$\therefore n(X)=25000$, $n(A)=13000$, $n(B)=10500$,
$n(A\cap B)=2500$
We have, $n(A\cup B)=n(A)+n(B)-n(A\cap B)$
$=13000+10500-2500=21000$
$\therefore$ Number of persons not reading any newspaper
$=n(X)-n(A\cup B)=25000-21000=4000$
Required percentage $=\frac{4000}{25000}\times 100=16\%$