Clock PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Clock-Based Reasoning for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This page provides detailed solutions, practice questions, and a free downloadable PDF to help you ace your UPSC preparation.

Why Clock Questions Matter in UPSC?

Clock-based questions are a crucial part of the UPSC CSAT (Civil Services Aptitude Test). They test your ability to:

➡️ Calculate angles between clock hands.
➡️ Determine time-based puzzles.
➡️ Solve complex reasoning problems involving clocks.

This page breaks down the concepts and provides year-wise solved questions to help you master this topic.

Key Concepts in Clock Reasoning

Before diving into the questions, let’s quickly revise the key concepts:

1. Basics of a Clock

➡️ A clock is a circle divided into 12 hours and 60 minutes.
➡️ Each hour represents 30 degrees (360° ÷ 12 = 30°).
➡️ Each minute represents 6 degrees (360° ÷ 60 = 6°).

2. Angle Between Clock Hands

➡️ Hour Hand Movement: Moves 0.5 degrees per minute (30° per hour).
➡️ Minute Hand Movement: Moves 6 degrees per minute.
➡️ Formula to calculate the angle between the hour and minute hands:

Angle=∣30H−5.5M∣Angle=∣30H−5.5M∣

Where:

➡️ HH = Hour
➡️ MM = Minutes

3. Mirror and Water Images

➡️ Mirror Image: Subtract the given time from 11:60.
➡️ Water Image: Subtract the given time from 18:30.

Year-Wise Clock PYQs (2011-2024)

Q1. Assume that

1. The hour and minute hands of a clock move without jerking.

2. The clock shows a time between 8 o'clock and 9 o'clock.

3. The two hands of the clock are one above the other.

After how many minutes (nearest integer) with the two hands will be again lying one above the other? [CSAT 2014]

(a) 60

(b) 62

(d) 67

Solution:

Given that,

1. The hour and minute hands of a clock move without jerking.

2. The clock shows a time between 8 o'clock and 9 o'clock.

3. The two hands of the clock are one above the other.

Now,

If minute hand moves 60 minutes, the hour hand moves 5 minutes

Thus relative speed = 60 - 5 = 55 minutes

As the clock shows a time between 8 o'clock and 9 o'clock the meeting time = 60/55 = 1.09 hours

1.09 hr = 1.09 x 60 = 65.4 minutes

Approximately they would meet again after 65 minutes.

Hence option (c) is correct

Q2. Between 6 PM and 7 PM the minute hand of a clock will be ahead of the hour hand by 3 minutes at [CSAT 2015]

(a) 6:15 PM

(b) 6:18 PM

(d) 6:48 PM

Solution:

Given that,

Minute hand ahead of hour hand (m) = 3 minutes

Hour hand (h) = 6 PM

Now,

According to formula

(5h ± m) x (12/11)

(5 x 6 + 3) x (12/11) {the sign is positive because minute hand is ahead of hour hand} = 33 x 12/11 = 36 minutes

Therefore, Time = 6 : 36 PM

Hence option (c) is correct

Q3. A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock? [CSAT 2017]

(a) 20 seconds

(b) 24 seconds

(d) 30 seconds

Solution:

Given that,

A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on

It takes 12 seconds to strike at 5 o'clock.

Now,

At 10 o'clock it strikes 10 times

So time taken to strike 10 times = 2 x 12 (twice of the time taken for 5 o'clock) = 24 seconds

Hence option (b) is correct

Q4. A watch loses 2 minutes in every 24 hours while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24 hour clock is followed? [CSAT 2017]

(a) The two watches show the identical time again on completion of 30 days.

(b) The two watches show the identical time again on completion of 90 days.

(d) None of the above statements is correct.

Solution:

Given that,

A watch loses 2 minutes in every 24 hours

Another watch gains 2 minutes in every 24 hours

So the time difference between two watches = 4 minutes

Thus, everyday the time difference between two watches will be keep on increasing by 4 minutes

Identical time between the watches would be shown at = 24 hours = 24 x 60 = 1440 minutes

It takes 1 day to reach 4 min difference so, 1 min difference will be reached in = (1/4) day

Thus for 1440 min = 1440/4 = 360 days

Therefore it would take 360 days to again show identical time

Hence option (d) is correct

Q5. A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time? [CSAT 2019]

(a) 5:36 pm

(b) 5:30 pm

(d) 5:18 pm

Solution:

Given that,

A wall clock moves 10 minutes fast in every 24 hours.

Corrected set time at 8:00 a.m. on Monday

Now,

Correct clock time in a day = 24 x 60 = 1440 minutes

Fast clock time or incorrect time = 1450 minutes

Total number of hours from 8:00 a.m. Monday to 6 : 00 pm Wednesday = 24 + 24 + 10 = 58 hours

Total clock minutes = 58 x 60 = 3480 minutes

For 1440 minutes of correct clock the incorrect clock takes 1450 minutes

For 1 minute of incorrect clock = (1440/1450)

For 3480 minute of incorrect clock = 3480 x (1440/1450) = 3456 of correct clock

3456/60 = 57 hr 36 min

Thus the correct time = 5 : 36 pm

Hence option (a) is correct

Q6. At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other? [CSAT 2021]

(a) At 7:00 hours.

(b) Between 7:00 hours and 7:05 hours.

(d) Between 7:05 hours and 7:10 hours.

Solution:

Mathematical inference:

Angle covered by minute hand in 1 min = 360/60 = 6 degrees

Angle covered by hour hand in 1 hour = 360/12 = 30 degrees

Angle covered by hour hand in 1 min = 30/60 = 1/2 degrees

So the minute hand is ahead of hour hand in 1 min = 6 - (1/2) = 5 degrees or (11/2)

At 7: 00 hours the angle between Minute and hour hand = 360 - (7 x 30) = 150 degrees

To have an angle of 180 the minute hand needs to cover 30 degrees

Time required = 30/(11/2) = 60/11 = 5 minutes

Thus time is between 7:05 hours and 7:10 hours

Hence option (d) is correct

Logical inference:

The hour and minute hands of a clock needs to be perfectly opposite to one another to have an angle of 180 degrees with one another.

The minute hand is at 12 and the hour hand is at 7. Thus the angle between them is not 180 degrees. The hour hand has moved just past seven, while the minute hand has gone to one at 7:05 o'clock. They still make a less than 180° angle with each other.

Therefore the angle of 180 degrees should be between 7:05 hours and 7:10 hours.

Hence option (d) is correct

Q7. Consider the following statements: [CSAT 2022]

1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.

2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Solution:

Statement 1: Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.

The statement is correct as hour hand and minute hand both coincide. (In 60 minutes, hour hand will move 5 minutes space while the minute hand will move 60 minutes space)

Thus, In every 60 minutes minute hand gains 55 minutes on the hour hand

Thus 15 min are gained = 15 x (60/55) = 16.36 min

Thus they coincide at 3 : 16 : 36 PM

Hence statement 1 is correct

Statement 2: Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.

Minute and hour hand will definitely coincide every minute crossing each other.

Hence statement 2 is correct

Q8. How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds? [CSAT 2022]

(a) 11580x

(b) 11581x

(d) 694861x

Solution:

As we know:

Seconds in a minute = 60 sec

Seconds in a hour = 60 x 60 = 3600 sec

Seconds in a day = 60 x 60 x 24 = 86400 sec

In a week = 60 x 60 x 24 x 7 = 604800 sec

Thus seconds in total are there in x weeks, x days, x hours, x minutes and x seconds =

604800x + 86400x + 3600x + 60x +1x = 694861x

Hence option (d) is correct

Q9. What is the angle between the minute hand and hour hand when the clock shows 4:25 hours? [CSAT 2024]

(a) 12.5°

(b) 15°

(d) 20°

Solution:

Given that,

Clock shows = 4 : 25 hours

Now,

Movement of Hour hand in 60 min = 30°

1 min = 0.5°

So, 25 min = 25 x 0.5° = 12.5°

Thus the hour hand has moved 12.5°

Therefore the angle between minute and hour hand = 30° - 12.5° = 17.5°

Hence option (c) is correct

Alternate Formula

Angle = 30H -11/2 M (H =hour , M = minute)

Q10. How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)? [CSAT 2024]

(a) 3 times

(b) 4 times

(d) 6 times

Solution:

Given that,

Hour hand and minute hand w.r.t 10:00 am and 2: 00pm (same day)

Now,

In an hour the hour hand and the minute hand coincide 1 time

So,

From 10: 00am to 11: 00 am - 1 time

11: 00 am to 1:00 pm = 1 time (as from the hour hand will coincide with minute hand exactly at 12 so from 11 to 1 it is only 1 time)

1: 00pm to 2:00 pm = 1 time

Total = 3 times

Hence option (a) is correct

ANSWER KEY

1. C

2. C

3. B

4. D

5. A

6. D

7. C

8. D

9. C

10. A

Download Clock PYQs PDF

➡️ Download the complete set of Clock PYQs (2011-2024) with solutions in PDF format.
➡️ Click Here to Download PDF

FAQs on Clock Reasoning for UPSC

1. Is Clock Reasoning important for UPSC?

➡️ Yes, Clock Reasoning is a crucial topic for the UPSC CSAT paper. It tests your logical reasoning and problem-solving skills.

2. How to prepare for Clock Reasoning in UPSC?

➡️ Understand basic concepts like angle calculation, mirror images, and water images.
➡️ Practice PYQs regularly.
➡️ Use reliable resources like NCERT books and online platforms like iassetu.com.

3. What are the most frequently asked Clock Reasoning questions in UPSC?

➡️ Angle between clock hands
➡️ Mirror and water images of clocks
➡️ Time-based puzzles

Conclusion

Practicing Clock PYQs is essential for cracking the UPSC CSAT paper. This page provides year-wise solved questions, practice problems, and a free PDF download to help you prepare effectively. Bookmark this page and revisit it regularly for updates.

For more UPSC preparation resources, explore iassetu.com. Happy learning!