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 Band C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine?

To find the percentage of people who do not read any magazine, we first calculate the percentage of people who read at least one magazine using the principle of inclusion-exclusion for three sets. Let A, B, and C be the percentages of people reading magazines A, B, and C respectively. Given: P(A) = 45% P(B) = 55% P(C) = 40% P(A and B) = 30% P(B and C) = 15% P(A and C) = 25% P(A and B and C) = 10% The percentage of people who read at least one magazine (P(A or B or C)) is given by the formula: P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(A and C) + P(A and B and C) Substitute the given values into the formula: P(A or B or C) = 45 + 55 + 40 - 30 - 15 - 25 + 10 P(A or B or C) = 140 - 70 + 10 P(A or B or C) = 70 + 10 P(A or B or C) = 80% This means 80% of the population reads at least one magazine. To find the percentage of people who do not read any magazine, subtract this from 100%: Percentage not reading any magazine = 100% - P(A or B or C) Percentage not reading any magazine = 100% - 80% = 20% Therefore, 20% of the population does not read any magazine. Analyzing the options: A) 10% is incorrect. This is the percentage that reads all three magazines. B) 15% is incorrect. C) 20% is correct, as calculated above. D) 25% is incorrect. This is the percentage that reads magazines A and C. The final answer is C.