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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 (a) 210 (b) 290 (c) 180 (d) 260

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

Answers (1)

The answer is the option (b)

Total number of persons in a town = 840 \Rightarrow n(U) = 840
Number of students who read Hindi = 450 \Rightarrow n(H) = 450
Number of students who play English = 300 \Rightarrow n(E) = 300
Number of students who read both = 200 \Rightarrow n(H\cap E) = 200

            \begin{aligned} n(H\cup E) = n(H) + n(E) - n(H\cap E) &= 450+300 - 200 = 550 \\ n(H'\cap E') = n(U) - n(H\cup E) &= 840 - 550 = 290\end{aligned}

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