Question:
A watch, which gains uniformly, is 2 minutes slow at noon on Monday and is 4 minutes 48 seconds fast at 2 pm on the following Monday. At what time was it correct?
A watch, which gains uniformly, is 2 minutes slow at noon on Monday and is 4 minutes 48 seconds fast at 2 pm on the following Monday. At what time was it correct?
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For clock-related problems, calculate the total gain/loss over time and determine the rate per hour. Use this rate to find the exact correction time.
Updated On: Mar 25, 2025
- \( 2 \) pm on Tuesday
- \( 2 \) pm on Wednesday
- \( 3 \) pm on Thursday
- \( 1 \) pm on Friday
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The Correct Option is B
Solution and Explanation
The watch gains time uniformly. Given:
- At noon on Monday, it is 2 minutes slow.
- At 2 pm on the next Monday, it is 4 minutes 48 seconds fast.
Total time gained = \( 2 + 4.8 = 6.8 \) minutes over \( 7 \) days and \( 2 \) hours \( = 170 \) hours.
The watch gains per hour = \( \frac{6.8}{170} = 0.04 \) minutes.
To determine when the watch was correct:
- The watch was slow by 2 minutes initially.
- Time required to correct this = \( \frac{2}{0.04} = 50 \) hours.
Counting 50 hours from noon on Monday, we arrive at 2 pm on Wednesday.
- At noon on Monday, it is 2 minutes slow.
- At 2 pm on the next Monday, it is 4 minutes 48 seconds fast.
Total time gained = \( 2 + 4.8 = 6.8 \) minutes over \( 7 \) days and \( 2 \) hours \( = 170 \) hours.
The watch gains per hour = \( \frac{6.8}{170} = 0.04 \) minutes.
To determine when the watch was correct:
- The watch was slow by 2 minutes initially.
- Time required to correct this = \( \frac{2}{0.04} = 50 \) hours.
Counting 50 hours from noon on Monday, we arrive at 2 pm on Wednesday.
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