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Question

Two newspapers A and B are published in a city. It is known that 30% of the city population read A and 25% read B, while 10% read both A and B. Further, 20% of those who read A but not B look into sports news and 40% of those who read B but not A also look into sports news, while 50% of those who read both A and B look into sports news. Then the percentage of the population who look into sport news, is

A
15
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B
13
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C
17.5
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D
12.7
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Solution

The correct option is A 15
Let the population of the city be 100.
Then n(A)=30,n(B)=25,n(AB)=10


Percentage of population who look into sports news
=20100×n(AB)+40100×n(BA)+50100×n(AB)=1100[(20×20)+(40×15)+(50×10)]=15%

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