UPSC Prelims 2006 Q45: Science & Technology – Quantitative Aptitude
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?
- (a) Twelve minutes to three
- (b) Thirteen minutes to three
- (c) Fourteen minutes to three
- (d) Fifteen minutes to three
Answer: (c) Fourteen minutes to three
Explanation
Interchanging the hands of a watch at 9:14
Work in degrees (the hour hand moves 0.5 degrees per minute, the minute hand 6 degrees per minute).
| Step | Calculation |
|---|---|
| Original hour hand at 9:14 | 9 x 30 + 14 x 0.5 = 277 degrees |
| Original minute hand at 9:14 | 14 x 6 = 84 degrees |
| After interchange: hour hand | 84 degrees, which is about 2 hours 48 minutes |
| After interchange: minute hand | 277 degrees = 277 / 6, about 46.2 minutes |
The minute hand points at about 46 minutes past 2, i.e. about 2:46, fourteen minutes to three, the closest listed time.
Answer: (c) Fourteen minutes to three.
Why each option is right or wrong
- (a) Incorrect. Twelve minutes to three (2:48) matches only the hour hand's position, not the minute hand's.
- (b) Incorrect. Thirteen minutes to three (2:47) is farther from the minute hand's 46.2 minutes than 2:46.
- (c) CORRECT. Fourteen minutes to three (2:46) is the closest to the minute hand's new position of about 46.2 minutes.
- (d) Incorrect. Fifteen minutes to three (2:45) is farther from the 46.2-minute position.
Key point
With the hands interchanged at 9:14, the minute hand points near 46 minutes, so the watch shows about 2:46, fourteen minutes to three.
Remember
9:14 with hands swapped reads about 2:46, fourteen minutes to three.
Common mistakes
- Forgetting that the hour hand also moves 0.5 degrees per minute.
- Using the hour hand only and answering 2:48.
- Mixing degrees per minute for the two hands.
Exam tip
Convert hands to degrees: hour hand = 30h + 0.5m, minute hand = 6m.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Clocks)
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Clock)