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find angle between the hands of a clock at 5:15 by Clock Angle Formula

Interview PUZZLE: How many degrees are in the angle between the hour and minute hands of a clock when the time is quarter past 5 i.e. 5:15?


We will use simple clock angle formula to solve this problems.

First let’s find how many degrees are in 1 minute of the clock.

Since, minute hand, in 60 minutes covers 360 degree.

Hence, in 1 minute it will cover = 360/60 = 6 degree.

So, the formula is: 1 minute = 6 degree

Since clock time is quarter past 5 i.e. 5:15, let’s calculate the distance covered by hour hand when minute hand covers 15 minute. Using unity Rule:

When Minute hand covers 60 minutes, Hour hand covers 5 minute distance.

When Minute hand covers 1 minutes, Hour hand covers 5/60 minute

angle between clock hands puzzle

If Minute hand covers 15 minute, Hour hand covers (5/60)*15 = 5/4 minute


Total distance between Minute hand and Hour hand at 5:15 = 10 minute + 5/4 minute

= 45/4 minute.

So, the angle between hour hand and minute hand at 5:15

= 45/4 minute * 6 degree

= 67.5 degree.

Published inMathematical Puzzles

One Comment

  1. Habeeb Khan Pathan

    I guess, i can make it in a another form, of course many approaches are possible for the same problem..

    4:20 ->
    20mins hand contribution: 20* 6 = 120 deg
    remove hour contribution angle: 4* 5* 6deg = 120 deg
    remove the amount of hour moved for 20 deg, 20/60 *5*6 = 10deg

    120 deg -120 deg -10 deg = -10 deg

    As usual software programmer right, small python snippet:

    Min = input(“Enter the minutes: \n”)
    Hour = input(“Enter the hours: \n”)
    Angle = float(int(Min)*6) – float(int(Hour)*5*6) – float(int(Min)*0.5)
    print(“The Angle between hour hand and minute hand is:\n”,float(Angle))
    if Angle 0:
    print(“The Minute Hand is leading Hour hand”)
    print(“Time is 00:00”)

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