Tips, Tricks to Solve Clock Related Questions in Reasoning

Clocks are one of the important topics among the mental ability sections in many competitive exams like bank, SSC, RRB, PSC. It not only involves the in-depth logical analysis but also involves a detailed level of calculation to solve the questions in the right manner. Here in this article, we will understand the tips and tricks to solve clock related questions in reasoning. 

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Concept of Degrees with Different Hands of the Clock 

Hour Hand

• In 12 hours = 360 degree
• In 1 hour = 360 / 12 = 30 degree 
• 1 Hour = 30 degree 
• Now, 1 Hour = 60 min = 30 degree 
• 1 minute = 1/2 degree 

Minutes Hand 

• In 60 minutes = 360 Degree
• In 1 minute = 360 / 60 = 6 Degree 
• 1 minute = 6 degree

 Seconds Hand

• 60 Seconds = 360 Degree
•  1 sec = 360 / 60 = 6 Degree 
• 1 Second = 6 degree

 Points to remember

• Speed of the minute hand= 6° per minute.
• Speed of the hour hand= 0.5° per minute.
• The concept of relative speed is used to solve the questions on clocks. The relative speed of minute hand w.r.t hour hand=5.5° per minute.
•  The hands of the clock are perpendicular in 15 minutes spaces apart.
•  The hands of the clock are in a straight line when they coincide or opposite to each other. 
•  0 degree / 360-degree → overlap / coincide 180 degrees → opposite / straight 90 degrees → right angle 
•  The minute hand gains 55 minutes over hour hand per hour. So, x minute space to be gained by minute hand over hour hand can be calculated as x × (60/55) or x × (12/11)
• Every hour, both the hands coincide once. In 12 hours, they will coincide 11 times. It happens due to only one such incident between 12 and 1’o clock.
• If both the hour hand and minute hand move at their normal speeds, then both the hands meet after 65 minutes.

Check out this article to find the tips and tricks to solve calender problems

Types of question that can be asked 

1) The angle between the hands of the clock 

2) Time at a particular angle

3) Position of hands of the clock

4) Faulty clocks

5) Time gained or lost by the clock

6) Mirror / Water Image-based time

Now, let’s discuss each of them in detail:

Type 1: Angle between the hands of the clock

Example 1: What will be the angle made by the hands of the clock at 8:15? 

FORMULA: |(60H – 11M ) / 2|

Solution: Angle at 7:30 

(60 × 8 – 11 × 15) / 2

(480 – 165) / 2 = 315 / 2 = 157.5 degree

TRICK: Hour hand → 1 hour = 30 degree 

8 hour → 240 degree

 1 minute = 1/2 degree 

15 minute = 7.5 degree

 Minute hand → 1 minute = 6 degree

 15 minute = 90 degree 

Now, Angle made by hour hand – Angle made by minute hand Required Angle = 240 + 7.5 – 90 = 247.5 – 90 = 157.5 degree

 Type 2: Time at a particular angle

Example 1: When will the 90-degree angle be formed between 7:00 and 8:00?

 FORMULA: Angle between the two hands =  |(60H – 11M ) / 2|

ie 90 = 11/2M – 30H = 11/2M – 30 × 7

ie 90+210 = 11/2M

300=11/2M, M=600/11=54, and 6/11. past 7

Now, to find the 2nd  right angle between 7 and 8,

90 = 30H – 11/2M = 30×7-11/2M 

11/2M=210-90=120, hence M=240/11=21 and 9/11 min. past 7

Type 3: Position of hands of the clock

 Example 1: How many times a day do the hands of the clock make a 180-degree angle?

Needles meet each other

 Solution: Thus, 22 times a day 23 hands of the clock make a 180-degree angle. 

Type 4: Faulty clocks 

If a clock indicates 4 hours 10 minutes. When the correct time is 4, it is said that the clock is 10 min too fast. If it indicates 4:40 when the correct time is 5, it is said to be 20 minutes too slow.

Example 1: The clock was set on Thursday, at 4 am. If the clock gains 20 minutes per hour, what will be the time that the clock shows on Friday, 8: 30 pm?

Solution: The clock was set on Thursday, at 4 am. 

The time from Thursday, from 4 am to Friday at 8.30 pm = 40 hours, 30 min. 

The clock gains 20 minutes per hour. So the clock gains 810 min in 40 hours, 30 minutes. 

So the time that the clock will show on Friday, 8.30 pm = 8. 30 + 810 min = 10 am Saturday.

 Type 5: Time gained or lost by the clock 

These types of problems arise when a clock moves faster or slower than the expected pace. While solving these problems, it is best to keep track of the correct clock.

Example 1: A watch gains 5 seconds in 3 minutes and was set right at 8 am. What time will it show at 10 pm on the same day? 

Solution: The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour

From 8 am to 10 pm on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 pm, the watch would show 10 hours 23 minutes 20 seconds per minute. 

Type 6: Mirror / Water image-based time 

Mirror Image: If it is a 12 hours clock, then subtract the given time from 11:60 hrs. And if it is a 24 hours clock, then subtract the given time from 23:60 hrs. 

Example 1: If it’s 7:20 in the 12-hour clock then what will be the time in the mirror?

 Solution: For every mirror image based on a clock, If it is 12 hours clock, then subtract given timing from 11:60 hours, And if it is 24 hours clock, then subtract given timing from 23:60 hrs. Here, it is a 12-hour clock, hence, 11:60 – 7:20 = 4:40. Thus, the mirror image will show 4:40 in the clock.

 Water Image: If minutes are less than 30, then subtract given timing from 18:30 hrs. If minutes are more than 30, then subtract given timing from 18:90 hrs. 

Example 2: If the water image of the clock shows 4 hours 25 minutes, then what will be the actual time? 

Solution: For every water image based on a clock, If minutes given are less than 30, then subtract given timing from 18:30 hours.

 And if minutes given are more than 30, then subtract given timing from 18:90 hrs. 

Here, minutes are less than 30, hence, 18:30 – 4:25 = 14:05 i.e. 2 hours 5 minutes.

Thus, the actual time shows 2 hours 5 minutes in a clock.

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