Clock Problems for SSC, Banking and Government Exams, Check How to Solve?

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Published on 11 August 2026 by

Key Takeaways

  • Clock Problems are crucial for SSC, Banking, and Government Exams, focusing on clock hand movement and angles.
  • Understanding a few key formulas helps candidates quickly solve most clock-related questions.
  • Candidates often need to calculate angles, the time of coincidences, and the distances traveled by clock hands using basic formulas.
  • The clock hands coincide 11 times every 12 hours and form right angles 22 times in that period.
  • Mastering Clock Problems allows candidates to navigate these topics efficiently in competitive exams.

Clock Problems for SSC, Banking and other Government Exams are an important part of the Reasoning and Quantitative Aptitude sections of many competitive examinations. Questions are generally based on the movement of the hour and minute hands, angles between clock hands, coincidence, opposite positions, right angles, and faulty clocks. Once candidates understand the basic formulas, most clock questions can be solved quickly without lengthy calculations.

What are Clock Problems?

Clock problems test a candidate’s ability to understand the movement and relative position of the hands of a clock. Most questions involve finding an angle, determining the time at which two hands meet, or calculating the gain or loss of a clock in SSC, Railways, Banking and other Government Exams. The basic movement of clock hands is given below.

Clock HandMovement
Hour Hand in 12 hours360°
Hour Hand in 1 hour30°
Hour Hand in 1 minute0.5°
Minute Hand in 1 hour360°
Minute Hand in 1 minute6°
Relative movement per minute5.5°
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What are the important Clock Formulas?

Candidates do not need to memorise a large number of formulas for clock questions. Understanding a few standard relationships is enough to solve most questions asked in competitive exams.

ConceptFormula
Hour hand movement0.5° per minute
Minute hand movement6° per minute
Relative speed5.5° per minute
Angle at H:M|30H − 5.5M|
Smaller angleMinimum of θ and 360° − θ
Hands coincideAngle = 0°
Hands oppositeAngle = 180°
Hands at right angleAngle = 90°

Here, H represents the hour and M represents the minutes.

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How do you find the angle between the hands of a clock?

The most common type of clock question asks candidates to calculate the angle between the hour and minute hands at a particular time. Use: Angle = |30H − 5.5M|

StepCalculationResult
Hour hand position30 × 3 + 0.5 × 30105°
Minute hand position6 × 30180°
Angle between the hands180° − 105°75°

If the calculated angle is greater than 180°, subtract it from 360° to obtain the smaller angle.

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How do you find the angle at an exact hour?

When the minute hand is at 12, the calculation becomes much easier because the hour hand moves by 30° for every hour. For example:

  • At 1:00 = 30°
  • At 2:00 = 60°
  • At 3:00 = 90°
  • At 4:00 = 120°
  • At 5:00 = 150°
  • At 6:00 = 180°

After 6:00, the smaller angle begins decreasing.

How many times do the hands of a Clock coincide?

The hour and minute hands do not meet exactly once every hour because the hour hand continuously moves while the minute hand tries to catch it. The hands coincide:

  • 11 times in 12 hours
  • 22 times in 24 hours

The time between two successive coincidences is approximately: 65 5/11 minutes

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How do you find when the clock hands coincide?

For finding the time when the hands meet between H and H+1, use: M = 60H/11. Example:

StepCalculationResult
FormulaM = (60 × H) / 11—
Substitute H = 5M = (60 × 5) / 11300/11
Convert into mixed fraction300/1127 3/11 minutes
Final Time5 hours + 27 3/11 minutes5:27 3/11

How many times are clock hands at right angles?

Clock hands form a right angle when the angle between them is 90°. In a normal clock:

  • They form a right angle 22 times in 12 hours
  • They form a right angle 44 times in 24 hours

How do you find when the hands are at 90 degrees?

For a right-angle question, use the general relationship: |30H − 5.5M| = 90 Solve for M to determine the required time. There can often be two right-angle positions within the same hour, so candidates should carefully read whether the question asks for the first or second occurrence.

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How many times are the clock hands opposite?

The hands are opposite when the angle between them is exactly 180°. They are opposite:

  • 11 times in 12 hours
  • 22 times in 24 hours

For such questions, use: |30H − 5.5M| = 180

What is the difference between smaller and reflex angles in Clock Problems?

Some questions specifically ask for the reflex angle instead of the smaller angle.

  • Suppose the smaller angle is 120°.
  • Then: Reflex Angle = 360° − 120° = 240°
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What is the difference between a Fast and Slow Clock?

A fast clock gains time, meaning it shows a later time than the actual time. A slow clock loses time, meaning it displays a time earlier than the actual time.

Clock TypeMeaning
Gains 5 minutesShows 5 extra minutes after the specified period
Loses 5 minutesFalls behind actual time by 5 minutes
Fast ClockDisplayed time is ahead
Slow ClockDisplayed time is behind

How do you solve questions on the distance travelled by clock hands?

When the length of a clock hand is given, the tip of the hand moves along the circumference of a circle. Use: Circumference = 2πr. Example:

StepCalculationResult
Length of minute handRadius = 10 cm10 cm
Distance in 1 full rotation2πr2π × 10
Distance travelled in 1 hour20π cm20π cm
Distance travelled in 30 minutesHalf of 20π10π cm

FAQs

Q1. What is the basic formula for clock problems?

For finding the angle between clock hands, use |30H − 5.5M|, where H is the hour and M is the number of minutes.

Q2. How many times do the hands of a clock coincide in a day?

The hour and minute hands coincide 22 times in 24 hours.

Q3. How many times do clock hands form a right angle in 24 hours?

The hands form a right angle 44 times in 24 hours.

Q4. What is the relative speed of the hour and minute hands?

The minute hand moves at 6° per minute and the hour hand at 0.5° per minute. Their relative speed is therefore 5.5° per minute.

Q5. Are clock problems difficult for competitive exams?

Clock problems are generally formula-based. Once candidates understand hand movement, angles and relative speed, most questions can be solved quickly.