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.