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 ?
- (a) 10%
- (b) 15%
- (c) 20% ✓ UPSC's answer
- (d) 25%
Why the answer is (c)
• Use the Principle of Inclusion-Exclusion to find the percentage of people reading at least one magazine: |A ∪ B ∪ C| = |A| + |B| + |C| - (|A∩B| + |B∩C| + |A∩C|) + |A∩B∩C|.
• Substitute the given values: 45 + 55 + 40 - (30 + 15 + 25) + 10.
• Calculate the sum of individual readers: 45 + 55 + 40 = 140.
• Calculate the sum of pairwise intersections: 30 + 15 + 25 = 70.
• Compute the union: 140 - 70 + 10 = 80%.
• The percentage not reading any magazine is 100% - 80% = 20%, which corresponds to option (c).
Why the other options are wrong
- (a) 10%
- 10% is the percentage of people who read all three magazines, not those who read none.
- (b) 15%
- 15% is the percentage of people who read magazines B and C, not those who read none.
- (d) 25%
- 25% is the percentage of people who read magazines A and C, not those who read none.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.