There can be different types of clock problems:
A few are mentioned here:
1. Finding angle (very common type and also, an important one)
2. Time taken for hands to travel certain angle
3. Faulty clocks (clocks gaining time or losing time) etc.
For most of these problems, you need to keep angular speed of hands in mind.
Some points to keep in mind:
1. Each hour is of 30 degrees. 3 hours make 90 degrees.
2. Hour hand moves 1/2 degrees per minute (30 degrees in one hour)
3. Minute hand moves 6 degrees per minute (360 degrees in one hour)
4. From one and two, minute hand is 12 times faster than hour hand.
5. A faulty clock which is gaining time, moves faster than expected.
A faulty clock which is losing time, moves slower than expected.
When a clock is faulty, both hands are faulty.
Most of the problems will be based on above points. Though not all problems are based on above points.
Now, let me take some examples and discuss.
1. Finding angle at 5:25.
Now, at 5:25, minute hand will be exactly on 5.
But hour hand will not be on 5 as it must have moved ahead by some angle.
Now, it has moved ahead for 25 minutes. And hour hand moves 1/2 degrees per minute. So, totaly, it has moved (1/2)*25 = 12.5 degrees.
2. Angle at 3:40.
Now, at 3:40, hour hand has moved 40 minutes i.e. it is 20 degrees ahead of 3. And minute hand is 150 degrees ahead of 3.
So, angle = 150 - 20 = 130 degrees.
3.
Dinesh started answering a test at a time between 3 pm and 4 pm. He noted the position of the hands of his watch. He ended the test at a time between 4 pm and 5 pm. The position of the hands were interchanged. For how many hours did the test last?
Options: 1)13/14 2)12/13 3)9/10 4)10/11 5)11/12
Let initial angular difference between two hands be x degrees.
Now, at the end of test, hour hand will move x degrees.
And minute hand will move (360-x) degrees. Both will do this journey in same time.
We know that minute hand is 12 times faster than hour hand.
So, 12*x = (360-x)
So, x=360/13
So, hour hand travels 360/13 degrees.
We know, in 1hour hour hand travels 30 degrees.
So, to travel 360/13, it will take 12/13 hours.
A few are mentioned here:
1. Finding angle (very common type and also, an important one)
2. Time taken for hands to travel certain angle
3. Faulty clocks (clocks gaining time or losing time) etc.
For most of these problems, you need to keep angular speed of hands in mind.
Some points to keep in mind:
1. Each hour is of 30 degrees. 3 hours make 90 degrees.
2. Hour hand moves 1/2 degrees per minute (30 degrees in one hour)
3. Minute hand moves 6 degrees per minute (360 degrees in one hour)
4. From one and two, minute hand is 12 times faster than hour hand.
5. A faulty clock which is gaining time, moves faster than expected.
A faulty clock which is losing time, moves slower than expected.
When a clock is faulty, both hands are faulty.
Most of the problems will be based on above points. Though not all problems are based on above points.
Now, let me take some examples and discuss.
1. Finding angle at 5:25.
Now, at 5:25, minute hand will be exactly on 5.
But hour hand will not be on 5 as it must have moved ahead by some angle.
Now, it has moved ahead for 25 minutes. And hour hand moves 1/2 degrees per minute. So, totaly, it has moved (1/2)*25 = 12.5 degrees.
2. Angle at 3:40.
Now, at 3:40, hour hand has moved 40 minutes i.e. it is 20 degrees ahead of 3. And minute hand is 150 degrees ahead of 3.
So, angle = 150 - 20 = 130 degrees.
3.
Dinesh started answering a test at a time between 3 pm and 4 pm. He noted the position of the hands of his watch. He ended the test at a time between 4 pm and 5 pm. The position of the hands were interchanged. For how many hours did the test last?
Options: 1)13/14 2)12/13 3)9/10 4)10/11 5)11/12
Let initial angular difference between two hands be x degrees.
Now, at the end of test, hour hand will move x degrees.
And minute hand will move (360-x) degrees. Both will do this journey in same time.
We know that minute hand is 12 times faster than hour hand.
So, 12*x = (360-x)
So, x=360/13
So, hour hand travels 360/13 degrees.
We know, in 1hour hour hand travels 30 degrees.
So, to travel 360/13, it will take 12/13 hours.
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