Assume that 1. the hour and minute hands of a clock move without jerking. 2. the clock shows a time between 8 o'clock and 9 o'clock. 3. the two hands of the clock are one above the other. After how many minutes (nearest integer) will the two hands be again lying one above the other ?
- (a) 60
- (b) 62
- (c) 65 ✓ UPSC's answer
- (d) 67
Why the answer is (c)
• The minute hand moves at 6° per minute and the hour hand at 0.5° per minute, so the minute hand gains 5.5° per minute on the hour hand.
• For the hands to be one above the other again, the minute hand must gain a full 360° relative to the hour hand.
• Required time = 360° / 5.5° per minute = 720/11 minutes = 65.4545... minutes.
• The nearest integer to 65.4545 is 65.
• Therefore option (c) 65 follows.
Why the other options are wrong
- (a) 60
- 60 minutes gives only 330° of relative gain, not the 360° needed for another overlap.
- (b) 62
- 62 minutes gives 341° of relative gain, which is short of the 360° needed for another overlap.
- (d) 67
- 67 minutes gives 368.5° of relative gain, which exceeds 360° and is not the nearest integer to 720/11.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.