A watch loses 2 minutes in every 24 while another watch gains 2 minutes, in 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is
- AThe two watches show the identical time again on completion of 30 days
- BThe two watches show the identical time again on completion of 90 days
- CThe two watches show the identical time again on completion of 120 days
- DNone of the above statements correct.Correct
Explanation
Here's a brief explanation:
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Calculate the relative time difference: Watch 1 loses 2 minutes in 24 hours. Watch 2 gains 2 minutes in 24 hours. The difference between the two watches accumulates at a rate of 2 (gain) + 2 (loss) = 4 minutes every 24 hours.
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Determine the total difference for identical time: For two 24-hour clocks to show the identical time again, the total accumulated difference between them must be exactly 24 hours (or a multiple of 24 hours). 24 hours = 24 * 60 minutes = 1440 minutes.
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Calculate the number of days: Number of days = Total difference required / Difference per day Number of days = 1440 minutes / 4 minutes/day = 360 days.
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Analyze the options: A) The two watches show the identical time again on completion of 30 days. (Incorrect, it's 360 days) B) The two watches show the identical time again on completion of 90 days. (Incorrect, it's 360 days) C) The two watches show the identical time again on completion of 120 days. (Incorrect, it's 360 days) D) None of the above statements correct. (This is correct, as the actual time is 360 days)
Therefore, the correct statement is D.
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