Question

In a community of $175$ persons, $40$ read TOI, $50$ read the Samachar Patrika and $100$ do not read either. How many persons read both the papers?

• A. $16$
• B. $17$
• C. $15$
• D. $14$

Answer 1

The correct option is C $15$

Number of people who read $TOI$ $n\left(TOI\right)=40$

Number of people who read Samachar patrika, n(samachar patrika)$=50$

Number of people who do not read newspaper$=100$

Number of people who read newspaper $(A\cup B)=$Total number of people - people who don't read newspaper

$=175-100=75$

Number of persons who read both newspapers,

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$n(A\cap B)=40+50-75$

$n(A\cap B)=90-75=15$

Number of persons who read both newspapers$=15$