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Sets and Relations question

2019 · 9 Apr · Shift 2 · Q33
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Sets and Relations question

2019 · 9 Apr · Shift 2 · Q33

JEE MainMathematicsSets and RelationsMCQ+4 / −1
Two newspapers A and B are published in a city. It is known that 25% of the city populations 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 advertisement is :-
  1. A
    13.5
  2. B
    13
  3. C
    12.8
  4. D
    13.9
View written solutionFree

Correct answer: D

  1. Let the total population be 100%100\%100%.

  2. Given:

  • Readers of A=25%A = 25\%A=25%
  • Readers of B=20%B = 20\%B=20%
  • Readers of both A∩B=8%A \cap B = 8\%A∩B=8%

So,

  • Readers of only A=25−8=17%A = 25 - 8 = 17\%A=25−8=17%
  • Readers of only B=20−8=12%B = 20 - 8 = 12\%B=20−8=12%
  • Readers of both AAA and B=8%B = 8\%B=8%
  1. Now compute those who look into advertisements from each group:

  • From only AAA: 30%30\%30% of 17%17\%17% =30100×17=5.1%= \frac{30}{100} \times 17 = 5.1\%=10030​×17=5.1%

  • From only BBB: 40%40\%40% of 12%12\%12% =40100×12=4.8%= \frac{40}{100} \times 12 = 4.8\%=10040​×12=4.8%

  • From both AAA and BBB: 50%50\%50% of 8%8\%8% =50100×8=4%= \frac{50}{100} \times 8 = 4\%=10050​×8=4%

  1. Total percentage of population who look into advertisements: 5.1+4.8+4=13.9%5.1 + 4.8 + 4 = 13.9\%5.1+4.8+4=13.9%

  2. Therefore, the correct option is: 13.9\boxed{13.9}13.9​ which is option D\boxed{D}D​.

  3. Comparison with stored correct answer:

  • Stored correct answer: DDD
  • Derived answer: DDD

Hence, the derived answer agrees with the stored correct answer.

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