UPSC Prelims 2006 · General Studies
Question 45: Logical Reasoning and Mental Ability
A watch showed a time of fourteen minutes past nine (9 hrs 14 minutes). The positions of the hour-hand and the minute-hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following?
AnswerThe answer is (c).
At 9:14 the minute hand is at 14 x 6 = 84 degrees and the hour hand at 9 x 30 + 14 x 0.5 = 277 degrees. Swapped, the hour hand is at 84 degrees and the minute hand at 277 degrees. The minute hand at 277 degrees reads about 46 minutes past (277/6 = 46.2), and at 2:46 the hour hand sits at 83 degrees, only 1 degree from 84. So the closest time is 2:46, fourteen minutes to three.
Why each option is right or wrong
- (a) Twelve minutes to three (2:48) puts the minute hand at 288 degrees, 11 degrees away.
- (b) Thirteen minutes to three (2:47) is a worse fit than 2:46.
- (c) Correct: 2:46 puts both hands within about a degree of the required positions.
- (d) Fifteen minutes to three (2:45) puts the hour hand at 82.5 degrees and the minute hand at 270 degrees, a poorer fit.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.