Time and Angles-Aptitude Shortcut Formulae

CLOCK-ANGLES
  • The angle between hours and minutes for a given time x:y(x hours and y minutes) is |30*x-11*y/2|(absolute value)

this comes from the fact that a hour hand elapses 30 degrees for every hour(360/12) and minute hand elapses 6 degrees(360/60)..but for 6:50,the hour hand also elapses extra offset from its original position where it has to be there at 6:00 sharp..the offset is calculated as follows:
1.for every 60 minutes of minutes hand,hour hand elapses 1 hour..so distance travelled by hour hand when the minute hand travels 1 min is 1/60
2.so the offset is (50/60)*30 degrees for the hour hand
3.so the total angle covered by hour hand for 6:50 is 6*30 degrees+offset=180+25=205 degrees
4.angle covered by minute hand is 50*6 degrees=300 degrees
So,angle between them =300-205=95 degrees )

If  θ degrees is the angle between minutes and hours clock,then

θ= |30*x-11*y/2|     where,y=minutes elapsed and x=hours elapsed

θ=|30H-5.5M|

  • Hours hand rotates 30 degrees in a hour
  • Minutes hand rotate 6 degrees per minute
  • Hours hand rotate  0.5 degree in a minute
  • If the answer we get through the above process is not found in given answers then find 360-(answer we get).
  • If  θ is the angle we get from the process then its reflective angle is found by 360- θ.
  • If the hours hand and minutes hand are in straight line then the angle between them=180 degrees
  • If the hours hand and minutes hand are together then the angle between them=0 degrees
  • If we are unable to find the exact angle try to find

     θ= 30*H-5.5*M   and    θ= 5.5*M -30*H

We can see any of the answer obtainted in given options

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

What is the angle between the minute and the hour hand of the clock which shows 12:24?

The reflex angle between the hands of a clock at 10.25 is:

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

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