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This is an archive article published on July 13, 2024

UPSC CSAT Simplified: How to approach the Clock Problem? (Part 2)

Can you tell what is the angle between the minute and the hour hand of your clock? If you find this important question in your CSAT paper of UPSC, how will you solve it swiftly and accurately? Here's a method with examples.

UPSC CSAT Simplified : How to approach clock problem- part 2?

In this article, we will discuss a technique wherein, if given any random time, how can we determine the angle between the hour and the minute hand? (Image source: Freepik)

—Mudit Gupta

(Are you preparing for UPSC CSE 2025? You must not ignore the CSAT paper. UPSC Prelims 2024 had a clear message for students that CSAT practice has to be a constant part of preparation. So, UPSC Essentials’ special series ‘UPSC CSAT Simplified’ presents some important topics from the qualifying CSAT paper of UPSC prelims. The aim is to provide you with some tested methods to answer the questions correctly without wasting precious time.)

🚨 The Indian Express UPSC Essentials brings to you the July edition of its monthly magazine. Click Here to read. Share your views and suggestions in the comment box or at manas.srivastava@indianexpress.com🚨

The Clock Problem: Part 2

In the previous article, we read about the angular speed of the minute and hour hand. We also discussed how to determine (method) the time at which the minute and the hour hand will coincide. (CLICK HERE to REVISE)

In this article, we will discuss a technique wherein, if given any random time, how can we determine the angle between the hour and the minute hand?

EXAMPLE 1

upsc Csat simplified clock 2 image 1 mudit gupta

Image courtesy: Mudit Gupta

In the figure given above, the clock shows the time to be 1:15 and we are asked to find out the angle between the hour and the minute hand.

Even though going by the exact mathematical calculations, there is a long route to solve this question, but our objective requirements for the UPSC CSAT do not require us to delve into the detailed process. For your ease, we can solve this question using a simple shortcut formula as mentioned:

ANGLE = | 30H-(11/2)M|

In the formula given above:

H stands for the hour
M stands for the minutes
The entire formula is in the modulus operator. It means that after calculating the said expression, whether we get a positive answer or a negative answer, we have to neglect the sign and just consider the mathematical value of it.

Using the above shortcut formula, if we have to find out the time at 1:15, then:

H = 1
M = 15
Putting these values in the formula we get angle = 52.5 Degrees

EXAMPLE 2

Find the angle between the hour and the minute hand at 1:50.

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Image courtesy: Mudit Gupta

Since the time is 1:50, as per the formula given above,

H = 1
M = 50
Angle = |-245| Degrees
Please observe that the value in the modulus is coming out to be negative. But since we have used the modulus operator, we can safely neglect the negative sign and the answer will be 245 Degrees.

In this specific case, there is an observation: Even though we are getting the angle to be 245 degrees but there is one more answer possible in this case. Let us understand this through a diagram.

Image courtesy: Mudit Gupta

The 245-degree angle that we got from the formula was the obtuse angle, as shown in the figure above. In certain questions, you might not be given an option of 245 degrees and hence, in such cases, you can find out the acute angle simply by subtracting 245 degrees from 360 degrees (because one complete angle of a clock comprises of 360 degrees.)

Subtracting 245 degrees from 360 degrees we get 115 degrees, which is the acute angle between the minute and the hour hand, as shown in the figure above.

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Always note, that there can be two possible angles between the hour and the minute hand as depicted above.

Check your progress:

Using the above concept, please find out the obtuse and the acute angle between the hands of the clock at 4:40.

Previous Article in the UPSC CSAT Simplified series:

How to approach Reading Comprehensions?

How to approach ‘Cubes and Dice’ questions?

How to approach ‘Calendar’ questions? (Part 1)

6 Tips to score 66.67 and qualify Prelims 2024 CSAT paper

How to approach ‘Calendar’ questions? (Part 2)

Tips on Reading Comprehension passages

UPSC CSAT Simplified: How to approach the Clock Problem? (Part 1)

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(About our Expert: Mudit Gupta has been a mentor and faculty for the UPSC Civil Services exam for 8 years with expertise in CSAT, Polity, International Relations, and Current Affairs. He is known to break complex concepts into simpler ones that allow UPSC aspirants to develop a grip over the subject matter.)

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