In a certain city, only 2 newspapers A and B are published. It is known that 25% of the city population read A and 20% read 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?

Explanation

Let C = Set of people who read paper A
and D = Set of people who read paper B
Given, n(C ) = 25, n(D) = 20, `n(CnnD) = 8`
`therefore n(CnnD')=n(C)-n(CnnD)`
= 25 - 8 = 17
But total number of people who read A but not B = 30%
`therefore` Percentage of people reading A but not B = 30% of 17
`=(30xx17)/(100)=(51)/(10)`
and `n(C'nnD)=n(D)-n(CnnD)=20-8=12`
Also, total number of people who read B but not A = 40%
`therefore` Percentage of people reading B but not A = 40% of 12
`=(40xx12)/(100)=(24)/(5)`
and given total people who read A and B = 50%
`therefore` Total number of people who read A and B = 50% of 8
`=(50xx8)/(100)=4`
`therefore` Percentage of people reading an advertisement
`=(51)/(10)+(24)/(5)+4=13.9%`