When we do problems with subject as clock, the possible question can be asking the angle between minutes hand and Hour hand, giving the angle between minute hand and and asking about the time. Another pattern of question is based on time gap between two meeting of hour and minute hands.
Type 1
What is the angle between minute hand and hour hand when the time is 3.40 am?
Solution :
clock is 360 degree in angle. Time covered in 360 degree will be 12 hours by hour hand and not 24 hours. Hence AM/PM classification in the question is not important.
Minute hand will cover the same 360 degree on every 60 minutes.
So in one hour, hour hand will cover 360/12= 30 degrees. And in one minute it will cover half (1/2 degree)degree.
Similarly for Minute hand, 360/60=6 degree covered in one minute.
Now coming back to the question given above,
We have to find the angle between the two hands at 3.40:
For this,
We know 3 hours means, 3*30 degrees=90 degrees. Also we have to consider the 40 minutes and its impact on hour hand. In 40 minutes, hour hand would have covered another 40/2=20 degrees.
So the total angle covered by hour hand is 90 degree + 20 degrees= 110 degrees.
Moving to minutes hand,
6 degrees in a minute, hence in 40 minutes, the minute hand covers 40*6=240 degrees.
Now take the difference between minute hand and hour hand,
240 degrees - 110 degrees= 130 degrees.
And
if you are given a question like below,
What is the time between 3 and 4, when the angle between minute hand and hour hand is 130 degrees?
Just think reverse!
Now consider the below probelm
What will be the time lag between two meetings of hour hand and minute hand?
the simple method is this.
Think how many times in 12 hours the two hands meet!
it is 11 times. Because 12 happens two times and hence not 12, just 11.
So when in 12 hours , the two hands meet 11 times... what follows is the logic of finding time gap between two meetings.
And it is 12/11 hours. or in minutes 12*60/11 = 720/11= 65 5/11 minutes.
Type 1
What is the angle between minute hand and hour hand when the time is 3.40 am?
Solution :
clock is 360 degree in angle. Time covered in 360 degree will be 12 hours by hour hand and not 24 hours. Hence AM/PM classification in the question is not important.
Minute hand will cover the same 360 degree on every 60 minutes.
So in one hour, hour hand will cover 360/12= 30 degrees. And in one minute it will cover half (1/2 degree)degree.
Similarly for Minute hand, 360/60=6 degree covered in one minute.
Now coming back to the question given above,
We have to find the angle between the two hands at 3.40:
For this,
We know 3 hours means, 3*30 degrees=90 degrees. Also we have to consider the 40 minutes and its impact on hour hand. In 40 minutes, hour hand would have covered another 40/2=20 degrees.
So the total angle covered by hour hand is 90 degree + 20 degrees= 110 degrees.
Moving to minutes hand,
6 degrees in a minute, hence in 40 minutes, the minute hand covers 40*6=240 degrees.
Now take the difference between minute hand and hour hand,
240 degrees - 110 degrees= 130 degrees.
And
if you are given a question like below,
What is the time between 3 and 4, when the angle between minute hand and hour hand is 130 degrees?
Just think reverse!
Now consider the below probelm
What will be the time lag between two meetings of hour hand and minute hand?
the simple method is this.
Think how many times in 12 hours the two hands meet!
it is 11 times. Because 12 happens two times and hence not 12, just 11.
So when in 12 hours , the two hands meet 11 times... what follows is the logic of finding time gap between two meetings.
And it is 12/11 hours. or in minutes 12*60/11 = 720/11= 65 5/11 minutes.
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