Question

In a certain city only 2 newspapers A and B are published. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. What is the percentage of the population who read an advertisement?

Answer 1

Let A & B denote sets of people who read paper A & paper B respectively and in all there are 100 people, then $n\left(A\right)=25,n\left(B\right)=20,n(A\cap B)=8$

Hence the people who read paper A only i.e. $n(A–B)=n\left(A\right)–n(A\cap B)=25–8=17$.

And the people who read paper B only i.e. $n(B–A)=n\left(B\right)–n(A\cap B)=20–8=12$.

Now percentage of people reading an advertisement $=\left[\right(30\%of17)+(40\%of12)+(50\%of8\left)\right]\%$

$=13.9\%$