How many times during a 12 hour period does the hour hand and the minute hand of the clock cross each other?


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Answer:

11

Step by Step Explanation:
  1. The minute hand makes one full revolution every one hour. Therefore, it will make 12 revolutions in a period of 12 hours.
  2. During each revolution, the minute hand crosses the hour hand once. Therefore, if the hour hand remains fixed, it would cross the hour hand 12 times.
  3. But the hour hand does not remain fixed and makes one full revolution in 12 hours. This means, the total numbers of crossings made by the minute hand will be 1 less than the number of revolutions made by it. Therefore, the total numbers of crossings will be 11.
  4. For example, if we start at 12 midnight, the two hands will meet at: (approximately)
    12 AM
    1:05 AM
    2:10 AM
    3:16 AM
    4:22 AM
    5:27 AM
    6:33 AM
    7:38 AM
    8:43 AM
    9:48 AM
    10:54 AM

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