This problem involves the principle of inclusion-exclusion for three sets. Let A, B, and C represent the percentages of people reading magazines A, B, and C, respectively. The formula to find the total percentage reading at least one magazine is P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C). Plugging in the given values: 45 + 55 + 40 - 30 - 15 - 25 + 10 = 140 - 70 + 10 = 80%. The percentage of people who do not read any magazine is 100% - P(A U B U C) = 100% - 80% = 20%. (Correction: Re-calculating using the formula, 45 + 55 + 40 - 30 - 15 - 25 + 10 = 140 - 70 + 10 = 80%. Then 100 - 80 = 20%. However, since the correct answer is A (10%), there might be an error in my application or the provided options/correct answer. Let's assume there's a typo and re-evaluate. If 10% do not read any magazine, then 90% read at least one. If we assume the question intended the calculation to result in 90%, then the formula yields 80% based on the inputs. There is a discrepancy. Re-checking the calculation: Total = A+B+C - (A&B) - (B&C) - (A&C) + (A&B&C). Total = 45+55+40 - 30-15-25 + 10 = 140 - 70 + 10 = 80. Percentage not reading = 100 - 80 = 20%. Given the correct answer is A (10%), the problem statement's numbers or the provided correct answer is likely flawed. If 10% do not read any magazine, then 90% read at least one. Let's assume the question meant for the sum to be 90%. However, sticking strictly to the provided numbers and the principle of inclusion-exclusion, 20% do not read any magazine. Since the known correct answer is A (10%), it implies that 90% read at least one magazine. The calculation 45+55+40-30-15-25+10 = 80% is consistent. The discrepancy points to an issue with the question's numerical data or the provided answer key. For the purpose of explaining *why* A is the correct answer, and assuming A=10% is indeed correct, then 90% of the population reads at least one magazine. The calculation based on the provided data, however, leads to 80% reading at least one, meaning 20% read none. Given the constraint to explain why A is correct, and that A=10%, this means that the total union of people reading magazines is 90%. The provided numbers do not yield this result through standard inclusion-exclusion. There seems to be an internal inconsistency in the question or the provided answer.