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

Have you ever wondered by how many degrees the hour and the minute hand move every minute?

We know that hour hand moves by 360 degrees in 12 hours. Hence, using the unitary method, we know it will move by 30 degrees in 1 hour.

Image Courtesy: Mudit Gupta

• Angle made in 60 minutes by the hour hand = 30 degrees
• Angle made in 1 minute by the hour hand = ( 30/60) degrees = 0.5 degree

So, every minute, the hour hand moves by 0.5 degree.

Following the similar logic for the minute hand, we reckon that the minute hand makes an angle of 360 degrees every hour (because in 1 hour, it takes one complete round of the clock). Following the unitary method, if the minute hand makes an angle of 360 degrees in 60 minutes, then it will make an angle of 6 degrees every minute.

Image courtesy: Mudit Gupta

Though we have understood the basic hand movement of the clock, have you ever noticed that the clock’s minute and hour hands overlap frequently? To put it in other words, have you ever noticed that the angle made by the hour and the minute hand is at some specific time?

Image courtesy: Mudit Gupta

EXAMPLE:

Let us consider a question: At what time between 2:00 P.M. and 3:00 P.M. the minute and the hour hands will overlap?

So, we are given a time bracket of [2:00-3:00]. In this time range, consider the smaller number i.e. 2. Now, multiply 2 by (60/11).

(You might want to know the logic behind multiplying 2 by (60/11). It comes from certain mathematical calculations that are not required to solve the UPSC CSAT questions quickly. For the sake of speed, we can conveniently skip that calculation.)

Multiplying 2 by (60/11) we get (120/11).  This can further be written as 10(10/11). Once, you have done this calculation, we can interpret it as: 10(10/11) minutes after 2:00 P.M., the hour and the minute hand will coincide with each other.

So, to answer this question: At what time between 2:00 P.M. and 3:00 P.M. the minute and the hour hands will overlap?

Ans: 2:10 P.M. approximately.

Check your progress:

If you have understood this concept, please answer this question: Do the hour and the minute hands coincide between 3:15 P.M. and 3:16 P.M.?

(Hint: Try finding out the time between 3:00 P.M. and 4:00 P.M. at which the minute and the hour hands coincide).

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

(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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