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  4. 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

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Q. 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

Sets

Solution:

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 $= \frac{4000}{25000} \times 100 = 16\%$