# How many times between 2 oclock and 4 oclock does the minute hand and the hour hand will be at the right angle?

By the time the minute hand has gone all the way round the clock and is back at 12, one hour later (i.e., at 1 o'clock), the hour hand has moved to 1. Five minutes later, the minute hand reaches 1, but they don't quite meet there because the hour hand would have moved 1/12 of the distance between 1 and 2, to indicate 5 minutes past 1. So the next time after 12 that the minute hand is directly over the hour hand is a bit after 1:05 (we'll calculate the exact time a bit later).

Similarly, the next time it happens is a bit after 2:10. Then a bit after 3:15, and so on.

Note that each time they meet, the number of minutes past the hour keeps increasing, so the hour hand would have moved closer to the next number. After 11 o'clock, the minute hand has to travel all the way and by the time they meet it is has to be 12 o'clock again, since we know what the clock looks like at that time. So the two hands overlap 11 times in a 12 hour period. So, in a 24 hour period, they would overlap 22 times.

To answer the second part of the question, let's try to figure out the little bit of extra time the minute hand needs to catch up to the hour hand after every 1:05 hours. Well, after 12 o'clock there are eleven occasions when the two hands match up, and since the clock hands move at constant speeds, those 11 events are spread equally apart around the clock face, so they are 1/11th of an hour apart. That's 5.454545 minutes apart. In other words they meet every after every 1 hour and 5.454545 minutes.

The precise times they overlap (in hours) would be 1 + 1/11, 2 + 2/11, 3+ 3/11, all the way up to 11 + 11/11, which is 12 o'clock again.

Q. An analog clock is showing 2 o'clock right now. At what time will the hour and minute hands overlap next?

Q. What is the angle between the hour and minute hands at 4:10?

### Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

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

• Clock - Important Formulas
• Clock - General Questions

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