In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

(a) 15%
(b) 20% ✓ UPSC's answer
(c) 25%
(d) 35%

Why the answer is (b)

• Let the total number of students be 100.

• The number of students who passed in English is 80, so those who failed in English are 100 - 80 = 20.

• The number of students who passed in Hindi is 70, so those who failed in Hindi are 100 - 70 = 30.

• The number of students who failed in both subjects is given as 15.

• The number of students who failed in only English is (Total failed in English) - (Failed in both) = 20 - 15 = 5.

• The number of students who failed in only Hindi is (Total failed in Hindi) - (Failed in both) = 30 - 15 = 15.

• The total percentage of students who failed in only one subject is 5 + 15 = 20%, which corresponds to option (b).

Why the other options are wrong

(a) 15%: 15% is the percentage of students who failed in both subjects, not just one.
(c) 25%: 25% is the sum of students who failed in only English (5%) and those who failed in both (15%), or incorrectly calculated as 100 - 70 - 5.
(d) 35%: 35% is the sum of students who failed in English (20%) and those who failed in Hindi (30%) minus the overlap, but incorrectly adds the 'only one' categories to the 'both' category or miscalculates the union of failures.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.