Clock Problems: Concepts and Shortcuts

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Understanding Clock Reasoning
A clock’s dial is like a complete circle that can be divided into 12 equal parts, with each division representing different hours of the day. Each hour space is further subdivided into 5 spaces – this represents duration of 1 minute. There are typically 2 hands that rotate in a clock. Though in totality there are three hands, but the seconds hand is not that significant from the point of view of clocks aptitude questions. In an hour, the hour hand covers one of the 12 equal parts of the clock i.e. it covers(1/12)th of the circumference of the circle in an hour’s time. On the other hand, the minute hand covers exactly 1 circumference of the clock in one hour. Further, we can conclude that the time in which the minute hand covers one full circle, the hour hand covers only (1/12)th of the circumference.
Let us try to implement concept of relative speed. The time, in which the minute hand covers 360 degrees (60 minutes), the hour hand only covers 30 degrees (5 minutes). In terms of relative speed, the minute hand is moving at a relative speed of 55 minutes per hour ahead of the hour hand. Therefore in 1 minute, the minute hand covers a relative distance equivalent to(55/60) or (11/12) minutes or relative distance: distance covered by minute hand- distance covered by hour hand: 1-(1/120 = (11/12) minutes
Given below are other important points related to the concept of clocks. You should learn these points by heart to answer the problems on clocks.
Important Points and Shortcuts for Clock problems
  • Clock formula: 11/12. This is a very important point for solving aptitude questions on clocks.
  • As minute hand covers one full circle i.e. 360 degrees in one hour, that means it travels 360/60 = 6 degrees/min.
  • An hour hand covers one part of the 12 major parts of the circle which means it covers 360/12 = 30 degrees in one hour i.e. it travels 30/60 = 1/2 degree per min.
  • Now, the relative speed of the minute hand is 6 – 1/2 = 11/2 or 5.5 degrees. This 11/2 degrees will be useful in finding the angle between the two hands of the clock.
  • The complete circle has a total of 360 degrees and in terms of minute spaces, it has been divided into 60 minutes spaces, which means each minute space represents 360/60 = 6 degrees.
  • The complete circle has been divided into 12 equal bigger units also, which we call as hours. This further implies that every hour space covers a total of 360/12 = 30 degrees.
  • The hour hand and minute hand meet once every hour. But in a 12 hour period, they meet 11 times.
  • There is one angle of 180 degrees in every hour i.e. both the hands are in the straight line in the opposite direction, but in a twelve hour period it happens 11 times.
  • There are 2 right angles every hour, but in a 12 hour period there are 22 such angles.
  • If the two hands are moving at the normal speeds, they should meet after every 65 5/11 min.
  • Clock Aptitude Tricks -Short Cut - Between x and (x + 1) O’clock, the 2 hands will be ‘t’ min apart at (5x t) 12/11 past x.
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