Q38 / 90 · JEE Main 2019 (09 Apr Shift 2) · Mathematics

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:

  • A
    13.5
  • B
    12.8
  • Correct answer
    C
    13.9
  • D
    13

Solution

Let nA and nB be the percentage of population in a city who read newspaper A and B respectively.

Therefore, nA=25, nB=20 and nA∩B=8

Now, we know that

nA∩B¯=nA-nA∩B

⇒nA∩B¯=25-8

⇒nA∩B¯=17

And,

nA¯∩B=nB-nA∩B

⇒nA¯∩B=20-8

⇒nA¯∩B=12

Therefore, percentage of those who read advertisements is

=30% of nA∩B¯+40% of nB∩A¯+50% of nA∩B

=30100×17+40100×12+50100×8

=1390100

Total persons who look into advertisement =13.9%

Hence, the correct answer is option: 'C'.

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