Question

In a city, three daily newspapers $A,B,C$ are published. $42$% of the people in that city read $A$, $51$% read $B$ and $69$% 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. The percentage of persons who read all the three papers is

• A. $25$%
• B. $18$%
• C. $20$%
• D. none of these

Answer 1

The correct option is A $25$%

Let the number of persons in the city be $100$

Then we have

$n\left(A\right)=42,n\left(B\right)=51,n\left(C\right)-68;n(A\cap B)=30,n(B\cap C)=28,n(A\cap C)=36n(A\cap B\cap C)=100-8=92$

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

$-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$

Substituting the above value, we have

$\Rightarrow n(A\cap B\cap C)=92-161+94=92-67=25$

Hence $25$% of the people real all the three papers.