The total angle made by the minute hand during an hour is 360
If it takes 360 for an hours it will take 40/60 * 360 = 240
The angle between the hour hand the minute hand will therefore, be somewhere between (240 - 90) = 150
as the hour hand is between 3 and 4.The angle made by the hour hand when it moves from say 3 to 4 will be 30
That is the hour hand makes 30 during the course of an hour.
The hour hand will therefore, move 40/60 * 30 = 20
Therefore, the net angle between the hour hand and the minute hand will be 150 - 20 = 130
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Find the angle between the minute hand and hour hand of a click when the time is 7.20?
Angle traced by the hour hand in 12 hours = 360 degrees.
Angle traced by it in 7 hrs 20 min i.e. 22/3 hrs = [(360/12) * (22/3)] = 220 deg.
Angle traced by minute hand in 60 min = 360 deg.
Angle traced by it in 20 min = [(360/20) * 60] = 120 deg.
Therefore, required angle = (220 - 120) = 100deg.
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The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.
Time is 2:20. Position of the hands: Hour hand at 2 (nearly) and Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through 1/2 degrees in a minute.
Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees
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A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
145/6 hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = [24 * (6/145) * 29] hrs of the correct clock
= 28 hrs 48 min of the correct clock.
So, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
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The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time. How much of the day does the clock gain or lose?
In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand.
55 minutes are gained in 60 min.
60 min. are gained in [(60/55) * 60] min == 65 5/11 min.
But they are together after 65 min.
Therefore, gain in 65 minutes = (65 5/11 - 65) = 5/11 min.
Gain in 24 hours = [(5/11) * (60*24)/65] = 10 10/43 min.
Therefore, the clock gains 10 10/43 minutes in 24 hours.
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At what time between 2 and 3 o'clock will the hands of a clock together?
At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10
min space apart.
To be together, the minute hand must gain 10 minutes over the other hand.
Now, 55 minutes are gained by it in 60 min.
Therefore, 10 min will be gained in [(60/55) * 10] min = 10 10/11 min.
Therefore, the hands will coincide at 10 10/11 min. past 2.
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How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move
five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60
minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th
minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an
integral number of minutes between them.
i.e 5 positions
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At how many points between 10 O'clock and 11 O'clock are the minute hand and hour hand of a clock at an angle of 30 degrees to each other?
Between 10 and 11, the minute hand and hour hand are at an angle of 30 to each at 12/11 * 45 minutes past 10 = 49 1/11 minutes past 10.
The next time they will be at angle of 30 to each other will be at 11.
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