A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination?

(a) 100
(b) 120
(c) 150 ✓ UPSC's answer
(d) 300

Why the answer is (c)

• Let the maximum marks in the examination be denoted by $M$.

• The passing mark is defined as 40% of the maximum marks, which is $0.40M$.

• The student scored 30 marks and failed by 30 marks, meaning the passing mark is 30 marks higher than the student's score.

• Therefore, the passing mark is $30 + 30 = 60$ marks.

• Equating the two expressions for the passing mark: $0.40M = 60$.

• Solving for $M$: $M = 60 / 0.40 = 150$.

Why the other options are wrong

(a) 100: If the maximum marks were 100, the passing mark would be 40, and a student scoring 30 would fail by only 10 marks, not 30.
(b) 120: If the maximum marks were 120, the passing mark would be 48, and a student scoring 30 would fail by 18 marks, not 30.
(d) 300: If the maximum marks were 300, the passing mark would be 120, and a student scoring 30 would fail by 90 marks, not 30.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.