Question

In a town of $840$ persons, $450$ persons read Hindi, $300$ read English and $200$ read both. Then the number of persons who read neither is

• A. $210$
• B. $290$
• C. $180$
• D. $260$

Answer 1

Answer: (B)

Let $H$ and $E$ denote the number of persons who read Hindi and English newspaper respectively.
Given, total number of persons, $n(U)=840$
Total number of persons who read Hindi newspaper,
$n(H)=450$
Total number of persons who read English newspaper,
$n(E)=300$
and $n(H\cap E)=200$
$\because n(H\cup E)=n(H)+n(E)-n(H\cap E)=550$
$\therefore$ The number of persons who read neither of the newspaper
$=n(\bar{H}\cap \bar{E})=n(U)-n(H\cup E)=290$