Multiple choice

If the two incorrect watches are set at 12 : 00 noon at correct time, when will both the watches show the correct time for the first time given that the first watch gains 1 min in 1 hour and second watch loses 4 min in 2 hours :

  1. $6$ pm, $25$ days later
  2. $12 : 00$ noon, $30$ days later
  3. $12$ noon, $15$ days later
  4. $6$ am $45$ days later
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B Correct answer
AI explanation

The first watch gains 1 minute per hour, meaning it gains 24 minutes per day and will show the correct time again after 12 hours, which is 720 minutes, taking 720/24 = 30 days. The second watch loses 2 minutes per hour (4 minutes in 2 hours), meaning it loses 48 minutes per day and will show the correct time again when it loses 12 hours, which is 720 minutes, taking 720/48 = 15 days. The least common multiple of 30 and 15 is 30 days, meaning both watches will correctly show 12:00 noon simultaneously 30 days later.

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