A clock strikes once at 1 o’clock, twice at 2 o’clock and thrice at 3 o’clock, and so on. If it takes 12 seconds to strike at 5 o’clock, what is the time taken by it to strike at 10 o’clock?
- (a) 20 seconds
- (b) 24 seconds ✓ UPSC's answer
- (c) 28 seconds
- (d) 30 seconds
Why the answer is (b)
• UPSC's official answer is (b) 24 seconds, obtained by treating the striking time as proportional to the number of strikes: 5 strikes take 12 seconds, so 10 strikes take 12 × 10/5 = 24 seconds.
• A stricter reading counts the gaps between strikes: 5 strikes have 4 gaps, so each gap is 12 ÷ 4 = 3 seconds, and 10 strikes have 9 gaps, giving 9 × 3 = 27 seconds. 27 seconds is not among the options.
• Since none of the printed options matches the gap method, the proportional answer is the one UPSC accepted, and it is the answer scored in the exam: (b).
Why the other options are wrong
- (a) 20 seconds
- 20 seconds matches neither the proportional method (24) nor the gap method (27).
- (c) 28 seconds
- 28 seconds matches neither the proportional method (24) nor the gap method (27).
- (d) 30 seconds
- 30 seconds would need each of the 10 strikes to take 3 seconds; it matches neither method.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.