Clock Reasoning Tricks: Angle Between Hands, Overlap and Time Questions for SSC Exams

Clock reasoning is a formula-based topic, so it is easy to score. The usual questions are: "What is the angle between the hands at 4:20?", "When do the hands overlap?" and "How many times do the hands make a right angle in a day?". These clock reasoning tricks for SSC give the speeds of the hands, the angle formula, the facts to remember and solved examples.

Basic Facts of the Clock

Angle Formula

Angle between the hands at H hours and M minutes = | 30H − 5.5M |

• If the answer is more than 180 degrees, subtract it from 360 degrees to get the smaller angle.
• Use H = 12 as 0 in the formula for the 12 o’clock hour.

Solved Examples on Angle

Example 1. Find the angle between the hands at 3:30.
| 30 × 3 − 5.5 × 30 | = | 90 − 165 | = 75°.

Example 2. Find the angle between the hands at 4:20.
| 120 − 5.5 × 20 | = | 120 − 110 | = 10°.

Example 3. Find the angle between the hands at 7:45.
| 210 − 247.5 | = 37.5°.

Example 4. Find the angle between the hands at 9:15.
| 270 − 82.5 | = 187.5°. The smaller angle is 360 − 187.5 = 172.5°.

When Do the Hands Overlap?

After H o’clock, the hands overlap at 60H / 11 minutes past H. For example, after 4 o’clock the hands overlap at 240/11 = 21 and 9/11 minutes past 4. After 5 o’clock they overlap at 300/11 = 27 and 3/11 minutes past 5.

Important Counts

The hands overlap only once between 11 and 1 (at 12 o’clock), which is why the count is 11 and not 12.

Other Useful Facts

• The hands make a right angle at 3:00 and 9:00 exactly.
• The hands are opposite to each other at 6:00 exactly.
• The minute hand gains 55 minutes over the hour hand in 60 minutes, so the hands are together after every 65 and 5/11 minutes.

Quick Tips

• Remember the formula | 30H − 5.5M | and the two speeds (6 and 0.5).
• If the angle is more than 180, subtract it from 360.
• Learn the counts 11, 22 and 44.
• Use the overlap formula 60H / 11 for any hour.

Quick Revision Points

• Angle = | 30H − 5.5M |.
• The minute hand moves 6 degrees a minute and the hour hand 0.5 degree a minute.
• The hands overlap 22 times in a day.
• The hands make a right angle 44 times in a day.
• The hands overlap after every 65 and 5/11 minutes.

Practice Questions With Answers

1. Find the angle between the hands at 6:00.
   Answer: 180°
2. Find the angle between the hands at 3:00.
   Answer: 90°
3. Find the angle between the hands at 9:30.
   Answer: 105°
4. Find the angle between the hands at 12:30.
   Answer: 165°
5. Find the angle between the hands at 2:40.
   Answer: 160°
6. How many times do the hands overlap in a day?
   Answer: 22 times
7. How many degrees does the minute hand move in one minute?
   Answer: 6 degrees
8. How many times do the hands make a right angle in 12 hours?
   Answer: 22 times
9. Find the angle between the hands at 5:10.
   Answer: 95°
10. Find the angle between the hands at 1:15.
    Answer: 52.5°

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Reasoning notes page, read the previous topic Calendar Reasoning and the next topic Number Series Reasoning. The Clock and Calendar note has more practice, and the Mirror and Water Image note covers the clock mirror image.

Frequently Asked Questions

What is the formula for the angle between the clock hands?

The angle is | 30H minus 5.5M |, where H is the hour and M is the minutes.

How fast does the minute hand move?

The minute hand moves 6 degrees every minute.

How fast does the hour hand move?

The hour hand moves 0.5 degree every minute.

What is the angle at 3 o’clock?

The angle at 3 o’clock is 90 degrees.

How many times do the hands overlap in 12 hours?

They overlap 11 times in 12 hours.

How many times do the hands overlap in a day?

They overlap 22 times in 24 hours.

How many times do the hands make a right angle in a day?

They make a right angle 44 times in a day.

How do I find the time when the hands overlap?

After H o’clock they overlap at 60H divided by 11 minutes past H.

What if the angle is more than 180 degrees?

Subtract it from 360 degrees to get the smaller angle.

Is clock reasoning asked in SSC exams?

Yes. Clock questions are asked in reasoning papers, but the number changes from year to year.

How long should a clock question take?

About 30 seconds with the formula.

What is the common mistake in clock questions?

Forgetting the movement of the hour hand when the minutes are not zero.