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A watch, which gains uniformly, is 3 minutes slow at noon on Monday and is 3 minutes 48 seconds fast at 2 p.m. on the following Monday. What time was it correct?
  • a)
    2 p.m. on Tuesday
  • b)
    2 p.m. on Wednesday
  • c)
    3 p.m. on Thursday
  • d)
    1 p.m. on Friday.
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A watch, which gains uniformly, is 3 minutes slow at noon on Monday an...
Understanding the Watch's Gain
To solve the problem, we need to calculate the total time elapsed and the watch's uniform rate of gaining time.
Time Analysis
- The watch is 3 minutes slow at noon on Monday.
- It becomes 3 minutes 48 seconds fast at 2 p.m. the following Monday.
- The time period from the first Monday to the next Monday is 7 days (or 168 hours).
Converting Time Gains
- The total time gained by the watch:
- From being 3 minutes slow to being 3 minutes 48 seconds fast:
- Total gain = 3 minutes + 3 minutes 48 seconds = 6 minutes 48 seconds.
- Converting 48 seconds into minutes gives us: 48/60 = 0.8 minutes.
- Therefore, total gain = 6.8 minutes.
Calculating the Gain Rate
- Gain per minute = Total gain / Total time in minutes.
- Total time in minutes = 168 hours * 60 minutes/hour = 10,080 minutes.
- Gain rate = 6.8 minutes / 10,080 minutes = 0.000674 minutes gained per minute.
Finding the Correct Time
To find when the watch was correct, we must determine how long it takes for it to gain 3 minutes from being slow.
- Since the watch gains time uniformly, we can calculate the time when it was correct:
- Time to gain back the 3 minutes = 3 minutes / (0.000674 minutes gained per minute) ≈ 4442 minutes.
Converting Minutes to Days
- 4442 minutes = 74 hours and 2 minutes.
- From noon on Monday, adding 74 hours takes us to:
- 48 hours = 2 p.m. Wednesday.
- An additional 26 hours = 3 p.m. Thursday.
Conclusion
The watch was correct at 3 p.m. on Thursday, thus confirming that option 'C' is correct.
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