# How many minutes after 7 oclock will the hands of the clock be a together B opposite each other C at right angles with each other?

The minute hand's angular speed is 360 degrees per hour. or 6 degrees per minute The hour hand's angular speed is 360 degrees per 12 hours, which is equal to 30 degrees per hour, or 0.5 degrees per minute. The angle between the hands is either decreasing or increasing at the rate of 6-0.5 = 5.5 degrees per minute. At 5 o'clock the angle between the hands is 150 degrees. The angle between the hands is decreasing at 5.5 degrees per minute. The hands will be together when the angle between them decreases the entire 150 degrees to 0. That will be 150/5.5 = 27 3/11 minutes. [Notice that on the hands' way to being together from 5 o'clock, they were perpendicular at one instant.] Then after the hands are together, the angle between the hands begins increasing at 5.5 degrees per minute. They will be 90 degrees apart in 90/5.5 = 16 4/11 minutes. That will be the second time after five o'clock they were perpendicular. So the answer is 27 3/11 + 16 4/11 = 43 7/ll minutes. Edwin

### Exercise :: Clock - General Questions

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12.

The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

 A. 80° B. 75° C. 60° D. 105°

Explanation:

 Angle traced by hour hand in 17 hrs = 360 x 17 ° = 255°. 2 12 2

 Angle traced by min. hand in 30 min. = 360 x 30 ° = 180°. 60

Required angle = (255 - 180)° = 75°.

### Exercise :: Clock - General Questions

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16.

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

 A. B. C. D.

Explanation:

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

 15 min. are gained in 60 x 15 min = 16 4 min. 55 11

 The hands are coincident at 16 4 min. past 3. 11

 17. How many times do the hands of a clock coincide in a day? Answer: Option C Explanation: The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). AM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

### Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

6.

At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

 A. 5 min. past 7 B. C. D.

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o'clock, they are 25 min. spaces apart.

Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

 5 min. spaces are gained in 60 x 5 min = 5 5 min. 55 11

 Required time = 5 5 min. past 7. 11

7.

At what time between 5.30 and 6 will the hands of a clock be at right angles?

 A. B. C. 40 min. past 5 D. 45 min. past 5

Explanation:

At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

 40 min. spaces are gained in 60 x 40 min = 43 7 min. 55 11

 Required time = 43 7 min. past 5. 11