Question

What is the percentage of persons who read only two papers ?

• A. $19\%$
• B. $31\%$
• C. $44\%$
• D. None of the above

Answer 1

The correct option is A $19\%$

Let total numbers of people be 100, So for newspapers

$n\left(A\right)=42,n\left(B\right)=51,n\left(C\right)=68,n(A\cap B)=30$

$n(B\cap C)=28$

$n(A\cap C)=36$

Also given, $n(\overline{A\cup B\cup C)}=8$

$n(A\cup B\cup C)=100-n(\overline{A\cup B\cup C)}=100-8=92$

Also,

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

$92=42+51+68-30-28-36+n(A\cap B\cap C)$

$n(A\cap B\cap C)=25$

Now, for people who read only two papers$=n(A\cap B)+n(B\cap C)+n(A\cap C)-3n(A\cap B\cap C)$

$=30+28+36-75$

$=19$

Thus, $19\%$ people read only two newspapers.

Hence, A is correct.