SSC Clock Questions with Answers and Tricks

Clock questions are a classic part of the SSC reasoning section. They ask for the angle between the hour and minute hands, the time when the hands coincide or become perpendicular, the mirror image of a time and the correct time on a faulty clock. One question usually appears in some shifts of CGL, CHSL and MTS. This practice paper gives you 30 clock questions with answers and short solutions, with all the important formulas.

Practice Paper at a Glance

What Are Clock Questions? Basic Concept in Simple Words

A clock face is a circle of 360 degrees with 12 hour marks and 60 minute marks. The two hands move at different speeds.

• The minute hand moves 360 degrees in 60 minutes, which is 6 degrees per minute.
• The hour hand moves 360 degrees in 12 hours, which is 30 degrees per hour or 0.5 degrees per minute.
• The minute hand gains 5.5 degrees per minute on the hour hand (6 - 0.5), which is 55 minute spaces per hour.
• Each hour mark is 30 degrees apart and each minute mark is 6 degrees apart.

Formulas and Shortcut Tricks for SSC Clock Questions

• Angle between the hands at H hours M minutes = |30H - 5.5M| degrees. If the answer is more than 180, subtract it from 360.
• Hands coincide (angle 0) between H and H + 1 at M = 60H / 11 minutes past H. The hands coincide 11 times in 12 hours and 22 times in 24 hours.
• Hands at a given angle d: 5.5M = 30H +/- d, so M = (60H +/- 2d) / 11. Choose the value that lies between 0 and 60.
• Hands opposite (180 degrees) happens 11 times in 12 hours. Right angle (90 degrees) happens 22 times in 12 hours.
• Mirror image of a time = 11:60 minus the given time. For example, the mirror image of 4:20 is 11:60 - 4:20 = 7:40.
• Faulty clock: if a clock gains or loses a fixed number of minutes per hour, the clock time = true time +/- (hours x gain or loss).
• Minute hand ahead: the angle between the hands increases by 5.5 degrees every minute when the minute hand is moving away from the hour hand.
• Straight line means 180 degrees or 0 degrees (coincide).

Set 1: Angle Between the Hands (Q1–Q10)

Q1. Find the angle between the hour and minute hands at 3:00.
Answer: 90 degrees
Solution: |30 x 3 - 0| = 90 degrees.

Q2. Find the angle between the hour and minute hands at 6:00.
Answer: 180 degrees
Solution: |30 x 6| = 180 degrees.

Q3. Find the angle between the hour and minute hands at 9:00.
Answer: 90 degrees
Solution: |30 x 9| = 270. 360 - 270 = 90 degrees.

Q4. Find the angle between the hands at 4:20.
Answer: 10 degrees
Trick: |30 x 4 - 5.5 x 20| = |120 - 110| = 10 degrees.

Q5. Find the angle between the hands at 3:30.
Answer: 75 degrees
Solution: |90 - 5.5 x 30| = |90 - 165| = 75 degrees.

Q6. Find the angle between the hands at 7:15.
Answer: 127.5 degrees
Solution: |210 - 5.5 x 15| = |210 - 82.5| = 127.5 degrees.

Q7. Find the angle between the hands at 12:30.
Answer: 165 degrees
Solution: |0 - 5.5 x 30| = 165 degrees.

Q8. Find the angle between the hands at 5:10.
Answer: 95 degrees
Solution: |150 - 5.5 x 10| = |150 - 55| = 95 degrees.

Q9. Find the angle between the hands at 8:20.
Answer: 130 degrees
Solution: |240 - 5.5 x 20| = |240 - 110| = 130 degrees.

Q10. Find the angle between the hands at 10:10.
Answer: 115 degrees
Solution: |300 - 55| = 245. 360 - 245 = 115 degrees.

Set 2: Hand Positions and Special Times (Q11–Q20)

Q11. How many degrees does the minute hand move in 20 minutes?
Answer: 120 degrees
Solution: 6 x 20 = 120 degrees.

Q12. How many degrees does the hour hand move in 1 minute?
Answer: 0.5 degrees
Solution: 30 degrees per hour / 60 = 0.5 degrees per minute.

Q13. How many times do the hands of a clock coincide in 24 hours?
Answer: 22 times
Trick: The hands coincide 11 times in 12 hours, so 22 times in 24 hours.

Q14. How many times are the hands of a clock at right angles in 24 hours?
Answer: 44 times
Solution: They are at right angles 22 times in 12 hours, so 44 times in a day.

Q15. At what time between 4 and 5 will the hands coincide?
Answer: 21 9/11 minutes past 4
Trick: M = 60H / 11 = 240 / 11 = 21 9/11 minutes past 4.

Q16. At what time between 7 and 8 will the hands coincide?
Answer: 38 2/11 minutes past 7
Solution: M = 60 x 7 / 11 = 420 / 11 = 38 2/11 minutes past 7.

Q17. At what time between 4 and 5 will the hands be in the opposite directions (in a straight line)?
Answer: 54 6/11 minutes past 4
Solution: 6M - (120 + 0.5M) = 180, so 5.5M = 300 and M = 54 6/11 minutes past 4.

Q18. What is the mirror image of the time 4:20?
Answer: 7:40
Trick: 11:60 - 4:20 = 7:40.

Q19. How many times do the hands of a clock overlap between 12 noon and 12 midnight?
Answer: 11 times
Solution: The hands overlap at 12:00, about 1:05, 2:11 and so on. The twelfth overlap would be at 12:00 again, so there are 11 distinct overlaps in 12 hours.

Q20. At what time between 2 and 3 will the hands first be at right angles?
Answer: 27 3/11 minutes past 2
Solution: 6M - (60 + 0.5M) = 90, so 5.5M = 150 and M = 27 3/11 minutes past 2.

Set 3: Faulty Clocks, Mirror Images and Mixed Questions (Q21–Q30)

Q21. A clock loses 2 minutes every hour. It is set right at 8 AM. What time will it show at 8 PM (true time)?
Answer: 7:36 PM
Solution: In 12 hours it loses 24 minutes. It shows 8:00 PM - 24 minutes = 7:36 PM.

Q22. A clock is set right at 6 AM and gains 10 minutes in 24 hours. What time will it show when the true time is 6 PM?
Answer: 6:05 PM
Solution: In 12 hours it gains 5 minutes. It shows 6:05 PM.

Q23. A clock loses 5 minutes every hour and is set right at 12 noon. What time will it show when the true time is 11 PM?
Answer: 10:05 PM
Solution: In 11 hours it loses 55 minutes. It shows 11:00 PM - 55 minutes = 10:05 PM.

Q24. Find the angle between the hands at 2:45.
Answer: 172.5 degrees
Solution: |60 - 5.5 x 45| = |60 - 247.5| = 187.5. 360 - 187.5 = 172.5 degrees.

Q25. Find the angle between the hands at 1:40.
Answer: 170 degrees
Solution: |30 - 5.5 x 40| = |30 - 220| = 190. 360 - 190 = 170 degrees.

Q26. Find the angle between the hands at 9:45.
Answer: 22.5 degrees
Solution: |270 - 5.5 x 45| = |270 - 247.5| = 22.5 degrees.

Q27. What is the mirror image of 8:15?
Answer: 3:45
Solution: 11:60 - 8:15 = 3:45.

Q28. How many degrees does the hour hand move from 12:00 to 2:20?
Answer: 70 degrees
Solution: 2 hours 20 minutes = 140 minutes. The hour hand moves 140 x 0.5 = 70 degrees.

Q29. At what time between 3 and 4 will the hands be in a straight line (opposite)?
Answer: 49 1/11 minutes past 3
Solution: 6M - (90 + 0.5M) = 180, so 5.5M = 270 and M = 49 1/11 minutes past 3.

Q30. The hands of a clock are at right angles at 3:00. At what time will they next be at right angles?
Answer: 32 8/11 minutes past 3
Solution: 6M - (90 + 0.5M) = 90, so 5.5M = 180 and M = 32 8/11 minutes past 3.

Common Mistakes in Clock Questions

• Forgetting to subtract from 360 when the angle is more than 180.
• Using 6 degrees per minute for the hour hand instead of 0.5.
• Using the wrong formula for coinciding hands (60H / 11).
• Calculating the mirror image by subtracting from 12:00 instead of 11:60.
• Mixing the true time and the faulty clock time.
• Not checking that the minutes lie between 0 and 60.

How to Practice These 30 Questions

1. Memorise the three main formulas: angle, coincide and mirror image.
2. Solve Set 1 in 6 minutes to build speed in angle questions.
3. Draw a small clock for questions on opposite and perpendicular hands.
4. Solve Set 3 carefully and write the true time and the clock time separately.
5. Revise your mistakes after one day.

Related Topics to Study Next

• Calendar Questions
• Direction and Distance Questions
• Time, Speed and Distance Questions
• SSC Previous Year Papers

Frequently Asked Questions

What is the formula for the angle between clock hands?

Angle = |30H - 5.5M| degrees, where H is the hour and M is the number of minutes. If the angle is more than 180, subtract it from 360.

How many degrees does the minute hand move in one minute?

The minute hand moves 6 degrees per minute, and the hour hand moves 0.5 degrees per minute.

How many times do the hands coincide in a day?

The hands coincide 22 times in 24 hours (11 times in 12 hours).

How many times are the hands at right angles in a day?

The hands are at right angles 44 times in 24 hours (22 times in 12 hours).

What is the formula for the time when hands coincide?

Between H and H + 1 the hands coincide at 60H / 11 minutes past H.

How do I find the mirror image of a time?

Subtract the given time from 11:60. For example, the mirror image of 8:15 is 3:45.

How do I solve faulty clock questions?

Find the total time gained or lost by multiplying the rate per hour by the number of hours, then add it to or subtract it from the true time to get the clock time.

How many clock questions come in SSC exams?

Usually one question comes from clocks in some shifts of SSC CGL, CHSL and MTS reasoning.

What is the speed of the minute hand relative to the hour hand?

The minute hand gains 5.5 degrees per minute on the hour hand, or 55 minute spaces in an hour.

How should I prepare clock questions for SSC exams?

Learn the three formulas, solve one set daily, practise mirror-image and faulty-clock questions and take mixed reasoning tests.