Study Notes for CAT 2021: Clock

For one complete revolution of the second hand, the minute hand covers one-minute space and the time taken for this is called a minute. For one complete revolution of the minute hand, the hour hand covers five-minute spaces and the time taken for this is called an hour.

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

Important Pointers to master clock problems

• At any given point of time, the hour hand and the minute hand make an angle between 0° and 180° with each other.
• The angle covered by the 60-minute spaces on the face of the dial is 6°.
• The minute hand covers 6° per minute and the hour hand covers 30° per hour or per minute.
• In 60 minutes, the minute hand gains 55 minutes on the hour hand.
• In any one hour, the hour hand and the minute hand coincide exactly once.
• When the hour hand and the minute hand are at right angles, they are 15-minute spaces apart.
• When the hour hand and the minute hand are opposite each other, they are 30-minute spaces apart.
• The angle F between the hour hand and minute hand of the clock at any given point of time can be calculated using the given formula where,
  M = minutes
  H = hours

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