In a town, 45% population read magazine A, 55% read magazine B

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In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine?

  1. 15%
  2. 25%
  3. 10%
  4. 20%

Answer

n(A) = 45%; n(B) = 55%; n(C) = 40%

n(A ∩ B) = 30%; n(B ∩ C) = 15%; n(A ∩ C) = 25%

n(A ∩ B ∩ C) = 10%

n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

= 45 + 55 + 40 - 30 - 25 - 15 + 10 = 80

80% population read any magazine.

The correct option is D.