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?

Solution:

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

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

Result:

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”)
else:
print(“Time is 00:00”)