Question

In a city, three daily newspapers A, B, C are published, $42\%$ read A; $51\%$ read B; $68\%$ read C; $30\%$ read A and B; $28\%$ read B and C; $36\%$ read A and C; $8\%$ do not read any of the three newspapers.

What is the percentage of persons who read only one paper ?

• A. $38\%$
• B. $48\%$
• C. $51\%$
• D. None of the above.

Answer 1

Answer: (B)

$48\%$

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,

People who read only one paper $=n\left(A\right)+n\left(B\right)+n\left(C\right)-2n(A\cap B)-2n(B\cap C)-2n(A\cap C)+3n(A\cap B\cap C)$

$=42+51+68-60-56-72+75$

$=48$

Hence, B is correct.