Clock Reasoning Questions

A complete circle with 360 degrees is a clock. It’s divided into 12 equal pieces, each of which is 360/12 = 30 degrees.The minute hand takes one hour to complete a full circle, therefore it spans 360° in 60 minutes.

It covers 360/60 = 6° each minute in 1 minute.In addition, the hour hand only covers one of the twelve segments in an hour. This means it will cover 30 degrees in 60 minutes, or i.e. ½° per minute.   

This means that the minute hand’s relative speed is 6 – ½ = 5 ½ degrees. 

When solving problems with clocks, we will apply the concepts of relative speed and relative distance.

Clock Formula

60 minutes = 360 degrees = 1 hour.

1 minute = 6 degrees = 1 minute.

6° x 5 = 30° = 5 minutes in a 5-minute space.

15-minute gaps apart at a right angle or perpendicular

22 times in 12 hours or 44 times in 24 hours = right angle or perpendicular (1 day).

Straight Angle, Straight Line, or 180° = 30-minute intervals.

11 times in 12 hours or 22 times in 24 hours = straight angle (1 day).

In 12 hours, the angle drawn by the hour hand equals 360°.

60 minutes = 360° angle sketched by minute hand.

Hour hand speed = 0.5 dpm (degree per minute).

Minute hand speed = 6 dpm.

At N o’clock, the angle of the hour hand from vertical is 30N.

Some interesting facts regarding clocks

Both hands coincide once per hour. They will coincide 11 times in the next 12 hours. It happens because of a single incident that occurs between 12 and 1 o’clock.

When the hands are parallel or opposite to each other, they are in the same straight line.

They are 15-minute gaps apart when the two hands are at a right angle. 

They will make two right angles in one hour, and only 22 right angles after 12 hours. It happens because the minute and hour hands at 3 o’clock and 9 o’clock create right angles.

When the hands are facing each other, they are 30 minutes apart.Both hands will meet after 65 minutes if both the hour and minute hands move at their typical speeds.

Let’s use the aforementioned concept to answer some questions.

Example

1) When the time is 4:20, the angle between the minute hand and the hour hand of a clock is:

The hour hand was at 120 degrees at 4:00.The minute hand will span the distance using the concept of relative distance.

 = 110 degrees

The angle formed by the hour and minute hands is equal to 120-110 = 10 degrees.

2)When the time is 3:30, the angle between the minute hand and the hour hand of a clock is:

The hour hand was at 90 degrees at 4:00.The minute hand will span the distance using the concept of relative distance.

b  =165 degrees

The angle formed by the hour and minute hands is 165-90=75 degrees.

3) When the time is 7.20, what is the angle between the minute and hour hands of a clock?

Sol:

• In 12 hours, the angle delineated by the hour hand equals 360 degrees.

• It traced an angle in 7 hours. 20 minutes, 

or 22/3 hours = [(360/12) * (22/3)] = 220 degrees

• In 60 minutes, the angle indicated by the minute hand equals 360 degrees.

• In 20 minutes, it traced an angle of [(360/20) * 60] = 120 degrees.

• As a result, the needed angle is (220 – 120) = 100 degrees.

4) How many times a day do the clock hands cross in a straight line but in the opposite direction?

Every 12 hours, the hands of a clock point in opposite directions (in the same straight line). 

(Because they point in opposing directions between 5 and 7 o’clock only.)

As a result, the hands point in opposing directions 22 times per day.

Conclusion

The hours on a clock are divided into 12 equal parts. 3600 is the angle traversed in 12 divisions (hours).As a result, the angle covered in one hour is 360/12 = 30 degrees.

Thus, each clock needle travels 300 degrees to move from one division to the next, but it takes various amounts of time to do it.In 1 minute, the hour and minute needles traversed the following distance:

A minute needle travels 60 minutes in 60 minutes, while an hour needle travels 5 minutes in 60 minutes.

 In 60 minutes, the minute needle travels 55 minutes further than the hour needle.

It covers a 55-minute route in 60 minutes.As a result, it will cover a 1 minute distance in min.