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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
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Verified Answer
The correct answer is:
290
290
Suppose E is the set of persons who read English and $\mathrm{H}$ is the set of persons who read Hindi.
Here, $n(\mathrm{U})=840, n(\mathrm{H})=450, n(\mathrm{E})=300, n(\mathrm{H} \cap \mathrm{E})=200$
The number of persons who read neither $=n$
$$
\begin{aligned}
&=n(\mathrm{U})-n(\mathrm{H} \cup \mathrm{E})=840-[n(\mathrm{H})+n(\mathrm{E})-n(\mathrm{H} \cap \mathrm{E})] \\
&=840-(450+300-200)=840-550=290
\end{aligned}
$$
Here, $n(\mathrm{U})=840, n(\mathrm{H})=450, n(\mathrm{E})=300, n(\mathrm{H} \cap \mathrm{E})=200$
The number of persons who read neither $=n$
$$
\begin{aligned}
&=n(\mathrm{U})-n(\mathrm{H} \cup \mathrm{E})=840-[n(\mathrm{H})+n(\mathrm{E})-n(\mathrm{H} \cap \mathrm{E})] \\
&=840-(450+300-200)=840-550=290
\end{aligned}
$$
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