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Clock Running Fast and Running Slow

A clock is said to be running fast, when the time shown by that clock is more than the time shown by the correct clock. Similarly, the clock is said to be running slow, when the time shown by that clock is less than the time shown by the correct clock.

If a clock indicates the time 8:20, when the correct time is 8:10, we say that the clock is running 10 minutes fast. Similarly, if a clock indicates 8:00, when the correct time is 8:10, we say that the clock is running 10 minutes slow.

If a clock is running 5 minutes fast for each hour, we say that the clock is gaining time at the rate of 5 minutes per hour. Similarly, if a clock is running 2 minutes slow for each hour, we say that the clock is losing time at the rate of 2 minutes per hour.

The above discussion can be summarised as under, so that it can be easily remembered.
  1. The minute hand completes one revolution in one hour.
  2. The hour hand completes one revolution in 12 hours.
  3. In one day, the minute hand makes 24 revolutions and hour hand makes 2 revolutions.
  4. The angle between the minute hand and hour hand changes at the rate of 5.5° per minute.
  5. The angle between the minute hand and hour hand at t o’clock is (t × 30)° when ‘t’ is less than or equal to 6 and it is [360° − (t × 30)°] when ‘t’ is greater than 6.
  6. The minute hand and hour hand overlap 22 times in a day (or 11 times in a period of 12 hours). The time gap between two consecutive overlapping is 1 hour Description: 106435.png minutes (or Description: 106443.png hours).
  7. Between t o’clock and (t + 1) o’clock, the two hands of a clock overlap at Description: 106460.png hours or at Description: 106467.png minutes past t.
  8. The angle between the minute and the hour hands is 180° on 11 occasions in a period of 12 hours. The angle between the two hands is 90° on 22 occasions in a period of 12 hours.




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