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 advertisements is

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13.5

12.8

13.9

answer is C.

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Detailed Solution

Let the population of city be 100
then $n (A) = 25, n (B) = 20, n (A \cap B) = 8$
so $n (A \cap \bar{B}) = 17, n (\bar{A} \cap B) = 12$
according the question, percentage of the population who look into advertisement $= \frac{30}{100} \times n (A \cap \bar{B}) + \frac{40}{100} \times n (\bar{A} \cap B) + \frac{50}{100} \times n (A \cap B)$

$= \frac{30}{100} \times 17 + \frac{40}{100} \times 12 + \frac{50}{100} \times 8$ $= \frac{51 + 48 + 40}{10} = 13.9$

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