In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 both.
Question:

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

(a) 210

(b) 290

(c) 180

(d) 260

Solution:

Total persons in a town is 840

Let H denote set of persons who read Hindi

Let E denote set of persons who read English

Then n(⋃) = 840, n(H) = 450, n(E) = 300

Then n(H⋃E) = n(⋃) – n(H⋃E)

n(⋃) – [n(H) + n(E) – n(H⋂E)]

= 840 – [450 + 300 – 200]

= 840 – 550

n(H⋃E) = 290

Therefore, the number of persons who read neither is 290.

Hence, the correct answer is option B.

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