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 $68$% 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. The percentage of persons who read all the three papers is

• A. $25$%
• B. $18$%
• C. $20$%
• D. $30$%

Answer 1

Answer: (A)

$25$%

Let the no. of persons in the city be 100

Then we have,
$n\left(A\right)=42,n\left(B\right)=51,n\left(C\right)=68;$

$n(A\cap B)=30,n(B\cap C)=28,n(A\cap C)=36$

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

$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)$

Substituding the above values, we have

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

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

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

Therefore the number of people reading all the three news papers are

$25$ people in given $100$ people so it is $25\%$