Clock-Related Problems

Concepts related to clocks problems 

Here are some helpful concepts while using easy methods to solve clock-related problems.

• The clock’s dial is divided into 60 equal minute spaces
• 1-minute space is equal to age with a measure of 6°
• One hour is equal to a 60-minute space (360°). The hour hand covers 5 minutes spaces one time, i.e., 30°
• Clock hands remain perpendicular to each other, thus apart by 15-minute spaces
• The clock hands are in a straight line with each other when opposite. They are separated by 30-minute spaces

Important terms related to clocks

Minute space:

The clock’s dial is also the circumference divided into 60 equal parts. These are called minute spaces.

Minute gain:

On the minute hand, every 60 minutes gains 55 minutes on the hour hand by the hour. This is called minute gain. 

Overlap: 

Overlap is that moment in each hour when the minute hand and the hour hand coincide.

Straight line: 

The clock hands are in a straight line with each other when opposite. They are separated by 30-minute spaces.

Problem: Puzzle 

Puzzle problems related to clocks are designed to get a thorough judgment of logical reasoning. They can be tricky and lost by the very underestimated minute detail. This can be better understood by the example below:

Example: Find out the original time from the reflection produced by an analogue clock. Find the original time when the reflection indicates 2:30.

Solution: The real-time logical, thorough analysis will come out at 9:30. Its authenticity can be cross-examined by observing a clock striking 9:30 in the mirror.

Problem: Time when the angle is provided 

When the angles lying between the hands of the clock are not perfect, that is, 270°, 90°, and 180°, it is a more difficult task to solve these problems related to the clock. These problems can be easily addressed without much time consumption, with a trick. This trick comes in the form of an equation as mentioned below:

T = 2/11 [H*30±A]

,where:

T signifies the time it took to form the angle 

H signifies the present hour running. 

Problem: Correct vs Incorrect Clock

This type of problem includes a comparison between the inaccurate watch and the accurate watch. The inaccurate watch shows the wrong time, which is symbolic of the clock either going slow or faster than the exact time. The inaccurate watch can be either faster than the accurate clock by a few seconds, minutes, or hours or it can be slower for the same durations. 

Clock-Related Questions: Solved Examples

1. A clock is showing the time accurately at 8 am. How many degrees will the hour hand have to rotate to strike at 2 pm? 

Solution:

The complete angle that is traced by the hour hand within 12 hours is 360°. 

From 8 to 2, there are 6 hrs.

The complete angle that has been in 6 hrs by the hour hand =6*(360/12)= 6*(30) =180°

2. By 30 minutes past 5, how many degrees did the hour hand turn if the time now is 11 pm?

Solution:

At 5 o’clock, the hour hand points at 5, and therefore, have an angle of 30°*5=150°.

The hour hand is known to travel 1/2° in a minute. Within 30 minutes, it will travel 30 *(1/2°) = 15°. Adding both we get 150° + 15° = 165°

3. What is the count within a day for the clock hands to be in a straight line?

Solution:

The count within a day for the clock hands to be in a straight line (180°) will be 22 times within 24 hours. The hands also overlap (0°) 22 times within a day. Thus, the total straight lines with a day are 22+22 = 44.

4. Find out the angle between the hour hand and the minute hand of a clock. This clock is currently striking at 7:20.

Solution:

The complete angle that is traced by the hour hand within 12 hours is 360°. 

The complete angle that has been in 8 hrs and 20 minutes will be 22/3 hours = [(360/12) * (22/3)] = 220 °

The complete angle that is traced by the hour hand within 60 minutes is 360°. 

 The complete angle that has been in 20 minutes is [(360°/20°) * 60] = 120°.

Thus, desired angle = (220° – 120°) = 100°

Conclusion

Clocks run on very easy terminologies. These include the hour hand, the minute hand, and the second hand. There are other related terms, including minute space, minute gain, overlap, straight line, etc. Clock problems are no less logic-based than they are reasoning-based. There are also some easy methods to solve clock-related problems. These all together include an easy understanding of the various types of lock-related problems. Some common clock-related problems are the angle separating the hands of the clock, inaccurate clock, puzzles, etc.