Important Concepts to Remember when Solving Clocks Related Problems

Clocks are an essential part of quantitative ability in various aptitude tests. Concepts of clock reasoning including  anti-clockwise and clockwise directions of the clocks are crucial for students to understand. 

Clocks Reasoning or Clock Related Problems

A clock is a circular instrument with three hands, one for the hour, one for the minute, and one for the second. The 360 degrees of a clock are divided into 12 equal sections. The angle between consecutive divisions is calculated by dividing the clock’s total angle of 360° by the number of segments, 12. (360°)/12= 30° angle in between two successive divisions.

Angle Divisions of a Clock

According to a detailed examination of a clock, an annular space between two consecutive divisions has five more divisions. The distance between the two divisions is equal to 5 minutes. As a result, dividing 30° by five yields the angular measure.

Types of Clocks Reasoning

There are typically three types of Clock Reasoning. They are as follows –

Angle Based Clocks

In this type of clock reasoning, the main task is to calculate time by the provided angles or the angles between the hour and the minute hand based on the time provided.

Defective Clocks

As the name suggests, defective clocks are defective and showcase the wrong time. Students are asked to calculate time or angles based on the question with the defective time provided. This adds difficulty to the clock reasoning problems but it can be solved with enough practice.

Reflection Clocks

Reflection clocks are clock reasoning problems based on mirror or water reflection where we have to look out for the reflection and figure out the solution based on the given problems.

Important Tips for Clock Reasoning

• The clock hands are perpendicular at 15-minute intervals.
• The minute hand crosses 60-minute space in 1 hour, or 3600, while the hour hand traverses 5-minute space in 1 hour, or 300.
• 60-minute gaps trace a 3600-degree angle. As a result, 1-minute space travels at a 60-degree angle.
• The clock’s dial has a circular form and is divided into 60-minute divisions.
• When the clock hands coincide or are opposite, they form a straight line.
• The hands of the clock are linear, 30 minutes apart and opposite each other.
• For 22 times in 12 hours and 44 times a day, the clock hands are perpendicular.
• The clock hands are opposite each other 11 times in 12 hours and 22 times a day.
• Per hour, the minute hand gains 55 minutes over the hour hand.

Clock Related Examples

The time is 7 a.m., according to an exact clock. How many degrees will the hour hand rotate when the clock reads 1 p.m.?

Solution:

We know that the angle delineated by the hour hand in 12 hours equals 360 degrees.

There have been 6 hours between 7 a.m. and 1 a.m.

In 6 hours, the hour hand drew an angle of =6*(360/12)=180°.

When the time is 4:20, what is the angle between both the hour hand and the minute hand of a clock?

Solution:

The clock hand was at 120 degrees at 4:00 p.m.

The minute hand will cover =20*112 =110 degrees using the concept of relative distance.

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

The clock is set to 8 a.m. When the clock acquires 10 minutes in 24 hours, what time is it when the clock reads 1 p.m. the next day?

Solution:

The time from 8 a.m. to 1 p.m. the next day equals 29 hours.

This clock’s 24 hours 10 minutes equals the accurate clock’s 24 hours.

This clock’s 1456 hours equals the actual clock’s 24 hours.

This clock’s 29 hours = 24*6145*29 hours of the proper clock

= The correct time is 28 hours and 48 minutes.

As a result, the correct time after 8 a.m. is 28 hrs 48 min.

It’s been 48 minutes since 12 a.m.

When the time is 3.25, find the angle between the hour and minute hands of a clock.

Solution:

The Minute hand is at 12 o’clock, while the Clock hand is at 3. To reach the figure 5 to represent 25 minutes, the minute hand must sweep across (30 x 5), i.e. 150°.

The Hour hand will also revolve for 25 minutes at the same time. Starting at 3 o’clock, the hour hand shall cover an angle of (25 x 30) / 60 = 12.5 degrees.

As a result, the angle between the Hour and Minute hands is (60 – 12.5) = 47.5°.

Conclusion

Clocks form an integral concept in quantitative ability as well as logical reasoning. Besides that, It utilises different concepts of angles, mirror and water reflections, and others, which helps prepare such concepts better.