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
Let
\[ n(H)=450 \]
\[ n(E)=300 \]
\[ n(H\cap E)=200 \]
Using the formula,
\[ n(H\cup E)=n(H)+n(E)-n(H\cap E) \]
\[ =450+300-200 \]
\[ =550 \]
Therefore, number of persons reading neither:
\[ 840-550 \]
\[ =290 \]
Answer
\[ \boxed{290} \]
Correct option: (b)