Clock reasoning questions

Reasoning Updated 11 Oct 2026

These clock reasoning questions with solutions cover every type that appears in SSC, railway, bank and state exams. The 30 questions on this page include the angle between the hands, times when the hands coincide, oppose or form a right angle, mirror images of a clock, the speed of the hands, and fast and slow clocks.

Each answer has been calculated exactly, and every explanation uses the standard formula so you can solve similar clock questions quickly in the exam.

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Angle between the hands of a clock (easy)

Q1. What is the angle between the hour hand and the minute hand of a clock at 3:00?
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Answer: A. 90°
Angle = |30 x 3 - 5.5 x 0| = |90 - 0| = 90°.
Q2. What is the angle between the hour hand and the minute hand of a clock at 4:20?
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Answer: C. 10°
Angle = |30 x 4 - 5.5 x 20| = |120 - 110| = 10°.
Q3. What is the angle between the hour hand and the minute hand of a clock at 7:30?
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Answer: B. 45°
Angle = |30 x 7 - 5.5 x 30| = |210 - 165| = 45°.
Q4. What is the angle between the hour hand and the minute hand of a clock at 2:15?
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Answer: D. 22.5°
Angle = |30 x 2 - 5.5 x 15| = |60 - 82.5| = 22.5°.
Q5. What is the angle between the hour hand and the minute hand of a clock at 5:40?
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Answer: D. 70°
Angle = |30 x 5 - 5.5 x 40| = |150 - 220| = 70°.
Q6. What is the angle between the hour hand and the minute hand of a clock at 11:10?
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Answer: B. 85°
Angle = |30 x 11 - 5.5 x 10| = |330 - 55| = 275°, and the smaller angle is 360° - 275° = 85°.
Q7. What is the angle between the hour hand and the minute hand of a clock at 8:20?
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Answer: A. 130°
Angle = |30 x 8 - 5.5 x 20| = |240 - 110| = 130°.
Q8. What is the angle between the hour hand and the minute hand of a clock at 6:15?
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Answer: C. 97.5°
Angle = |30 x 6 - 5.5 x 15| = |180 - 82.5| = 97.5°.

When do the hands coincide, oppose or make a right angle (medium)

Q9. At what time between 4 and 5 o'clock do the two hands of a clock coincide?
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Answer: A. 21 9/11 minutes past 4
The hands coincide when 30 x 4 = 5.5m, so m = 120 / 5.5 = 240/11 = 21 9/11 minutes past 4.
Q10. Between 9 and 10 o'clock, at what time are the hour hand and the minute hand exactly together?
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Answer: C. 49 1/11 minutes past 9
The hands coincide when 30 x 9 = 5.5m, so m = 270 / 5.5 = 540/11 = 49 1/11 minutes past 9.
Q11. At what time between 7 and 8 o'clock are the hands of a clock in opposite directions?
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Answer: B. 5 5/11 minutes past 7
For opposite hands, 30 x 7 - 5.5m = 180, so 5.5m = 30 and m = 60/11 = 5 5/11 minutes past 7.
Q12. At what time between 2 and 3 o'clock are the hands of a clock at right angles?
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Answer: D. 27 3/11 minutes past 2
5.5m - 60 = 90 gives m = 150 / 5.5 = 27 3/11 minutes past 2. The other case, 60 - 5.5m = 90, gives a negative time, so this is the only right angle in that hour.
Q13. Apart from 3:00, at what time between 3 and 4 o'clock are the hands at right angles?
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Answer: D. 32 8/11 minutes past 3
5.5m - 90 = 90 gives 5.5m = 180, so m = 360/11 = 32 8/11 minutes past 3.
Q14. How many times do the hour hand and the minute hand coincide in a day of 24 hours?
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Answer: B. 22
The hands coincide 11 times in every 12 hours, because the meeting near 12 o'clock is shared by the 11 to 12 and 12 to 1 hours. So in 24 hours they coincide 22 times.
Q15. How many times are the hands of a clock at right angles in a day of 24 hours?
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Answer: A. 44
Between two meetings of the hands they form a right angle twice. There are 11 such gaps in 12 hours, giving 22 right angles, so there are 44 in a day.
Q16. How many times in a day of 24 hours are the hands of a clock in a straight line (either together or opposite)?
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Answer: C. 44
They coincide 22 times and point in opposite directions 22 times, so they are in a straight line 22 + 22 = 44 times.

Mirror image of clock questions (medium)

Q17. A clock shows 3:40. What time does its image in a plane mirror show?
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Answer: A. 8:20
For a mirror image, subtract the time from 11:60 (that is, 12:00): 11:60 - 3:40 = 8:20.
Q18. A clock shows 2:15. What time does its image in a plane mirror show?
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Answer: C. 9:45
For a mirror image, subtract the time from 11:60 (that is, 12:00): 11:60 - 2:15 = 9:45.
Q19. A clock shows 10:25. What time does its image in a plane mirror show?
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Answer: B. 1:35
For a mirror image, subtract the time from 11:60 (that is, 12:00): 11:60 - 10:25 = 1:35.
Q20. A clock shows 7:10. What time does its image in a plane mirror show?
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Answer: D. 4:50
For a mirror image, subtract the time from 11:60 (that is, 12:00): 11:60 - 7:10 = 4:50.
Q21. A clock shows 12:20. What time does its image in a plane mirror show?
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Answer: D. 11:40
For times between 12:00 and 1:00, subtract from 23:60: 23:60 - 12:20 = 11:40.
Q22. At which of these times does a clock and its mirror image show the same time?
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Answer: B. 6:00
11:60 - 6:00 = 6:00, so at 6:00 the mirror shows the same time. At 3:00 the mirror shows 9:00 and at 4:30 it shows 7:30.

Speed of clock hands

Q23. Through what angle does the hour hand move in 2 hours 20 minutes?
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Answer: A. 70°
The hour hand moves 0.5° per minute. 140 minutes x 0.5° = 70°.
Q24. Through what angle does the minute hand move in 25 minutes?
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Answer: C. 150°
The minute hand moves 6° per minute, so 25 x 6° = 150°.
Q25. After how many minutes do the hands of a correct clock meet again?
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Answer: A. 65 5/11 minutes
The minute hand gains 5.5° per minute on the hour hand. To gain a full 360°, it takes 360 / 5.5 = 720/11 = 65 5/11 minutes.
Q26. How many degrees does the minute hand gain over the hour hand in 12 minutes?
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Answer: C. 66°
Relative speed = 6° - 0.5° = 5.5° per minute, so in 12 minutes it gains 5.5 x 12 = 66°.

Fast and slow clock questions (hard)

Q27. A watch loses 5 minutes every hour. It is set right at 8 a.m. What time will it show at 8 p.m. on the same day?
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Answer: B. 7 p.m.
In 12 hours it loses 12 x 5 = 60 minutes, so it shows 8 p.m. - 1 hour = 7 p.m.
Q28. A clock gains 10 minutes every 24 hours. It is set right at noon on Monday. What time will it show at noon on Thursday?
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Answer: D. 12:30 p.m.
Monday noon to Thursday noon is 3 days, so it gains 3 x 10 = 30 minutes and shows 12:30 p.m.
Q29. The hands of a faulty clock meet every 64 minutes of correct time. How much does the clock gain in a day?
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Answer: D. 32 8/11 minutes
In a correct clock the hands meet every 720/11 minutes. The faulty clock's hands meet 16/11 minutes early, so it gains 16/11 minutes in every 64 minutes. In 1,440 minutes it gains (16/11) x (1440/64) = 32 8/11 minutes.
Q30. A clock gains 3 minutes every hour. It is set right at 10 a.m. What is the correct time when it shows 4:18 p.m. the same day?
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Answer: B. 4 p.m.
The clock shows 63 minutes for every 60 real minutes. From 10 a.m. to 4:18 p.m. it shows 378 minutes, which is 378 x 60 / 63 = 360 real minutes, so the correct time is 4 p.m.

How to prepare

Most clock questions use two facts: the minute hand moves 6° per minute and the hour hand moves 0.5° per minute, so the minute hand gains 5.5° every minute. The angle between the hands at h hours m minutes is |30h - 5.5m|; if the result is more than 180°, subtract it from 360° to get the smaller angle.

To find when the hands make a given angle A between h and h + 1 o'clock, solve 5.5m = 30h ± A. The hands meet 22 times a day, are opposite 22 times and are at right angles 44 times. For a mirror image, subtract the time from 11:60. For fast or slow clocks, work out how many minutes are gained or lost per hour and scale up to the period asked.

Study tips

Learn the formula |30h - 5.5m| and practise it on any time you see on a clock.
Always check whether the question wants the smaller angle or the reflex angle.
Keep answers as fractions like 21 9/11 instead of rounding, because exam options use exact values.

Questions people ask

What is the formula for the angle between clock hands?

The angle at h hours and m minutes is |30h - 5.5m| degrees. If the answer is more than 180°, subtract it from 360° to get the smaller angle.

How many times do clock hands overlap in a day?

The hands overlap 11 times in 12 hours and 22 times in 24 hours. They meet once every 720/11 minutes, that is 65 5/11 minutes.

How do I find the mirror image of a clock time?

Subtract the given time from 11:60. For example, the mirror image of 3:40 is 11:60 - 3:40 = 8:20.

How do I solve clock reasoning questions quickly?

Remember that the minute hand gains 5.5° per minute over the hour hand and set up a single equation for the angle you need. Most clock questions are solved in one or two steps with this idea.

Every question on this page is written and fact-checked by the GK Quizzes team. Spotted a mistake? Tell us and we will fix it. How we make our questions.