Two newspapers A and B are published in a city. It is known that 25 % of the city population reads A and 20 % reads B while 8 % reads both A and B . Further, 30 % of those who read A but not B look into advertisements and 40 % of those who read B but not A also look into advertisements, while 50 % of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisemen

Step-by-step solution

Let n A and n B be the percentage of population in a city who read newspaper A and B respectively. Therefore, n A = 25 , n B = 20 and n A ∩ B = 8 Now, we know that n A ∩ B ¯ = n A - n A ∩ B ⇒ n A ∩ B ¯ = 25 - 8 ⇒ n A ∩ B ¯ = 17 And, n A ¯ ∩ B = n B - n A ∩ B ⇒ n A ¯ ∩ B = 20 - 8 ⇒ n A ¯ ∩ B = 12 Therefore, percentage of those who read advertisements is = 30 % of n A ∩ B ¯ + 40 % of n B ∩ A &#