Clock based math problems are among the most challenging and interesting problems to crack.
Basics
For every 60 units that a minute hand move in an hour , the hour hand moves 5 units.
For 12 hours the hour hand completes 360 degrees
1 hour = 360/12 = 30 degrees
60 minutes = 30 degrees
Degrees turned by hour hand in 1 minute = 0.5 degrees
For 1 hour the minute hand completes 360 degrees
1 hour = 360 degrees
60 minutes = 360 degrees
Degrees turned by minute hand in 1 minute = 6 degrees
Lets test what we have learned:
Q) Find the degree between hour hand and minute hand at 3:32'
Hour hand = 3
1 minute ( hour hand) = 0.5 degrees
3 hours = 3*0.5*60(1 hour= 60 minutes)
3 hours ( 3'o clock) = 90 degrees
Minute Hand = 32'
1 minute(minute hand) = 6 degrees
32 minutes(minute hand) = 32*6 = 192 degrees
For the 32 minutes, the hour hand moves by an additional 16 degrees
= 32*0.5
So Hour hand at 32 minutes = 90+16=106 degrees
Degrees between minute hand and hour hand at 3:32' = 192-106
=86 degrees
Number of right angles
1) A clock makes two right angles between 2 hours
2) The clock does not makes 48 right angles in 24 hours( 1 day)
P.S: Between 2 -4 and 8-10 there are 3 right angles and not 4
The first right angle between 3 - 4 (9-10) and second right angle bw:
2-3(8-9) are the same.
Q) At what time between 3 and 4 p.m is the first right angle formed
At 3 p.m
No of units that the hour hand is ahead of the minute hand = 15 units
For 90 degrees the minute hand should be 15 units ahead of hour hand
No of units that the minute hand has to cover = 15+15 = 30 units
Distance covered by minute hand over hour hand in one hour = 55 units
1 hour = 55 units
x hour = 30 units
x = 30/55 = 6/11 of an hour
So first right angle between 3 and 4 is at 6/11 of an hour
Converting 6/11 to minutes = 6/11 * ( 60) minutes
= 360/11 minutes
= 32 ( 8/11) minutes
Converting 8/11 minutes to seconds = 8/11*(60) = 480/11 = 43.6363..
So the first right angle is at 3 : 32 : 43.64
Learn how to Solve Tricky Clock Angle Math Problems
