Clock: Meaning, Reasoning Questions and Answers, Formula

What is Clock Reasoning?

Clock reasoning is an important topic in quantitative aptitude and logical reasoning that focuses on solving problems related to time, angles, and the movement of clock hands. In simple terms, clock reasoning questions require you to analyze how the hour hand and minute hand move and form angles at different times. These questions are widely asked in competitive exams and are considered both conceptual and scoring when formulas are applied correctly.

Definition of Clock Problems in Aptitude

Clock problems are a type of aptitude reasoning questions where you are given a specific time or condition and asked to calculate angles, positions, or time intervals on a clock.

• These questions involve time-based calculations and angle reasoning
• You may be asked to find the angle between clock hands, the time when hands coincide, or when they are opposite
• They test your understanding of time and motion in a circular path

Example:
At 3:00, the minute hand is at 12 and the hour hand is at 3. The angle between them is 90°.

Concept of Time, Angles, and Movement of Hands

To solve clock reasoning questions easily, you must understand how the hands of a clock move:

• A clock is divided into 360 degrees
• There are 12 numbers, so each number represents 30 degrees
• The minute hand moves faster than the hour hand
• The hour hand moves slowly and continuously, not in jumps

Key concepts:

• Minute hand covers 360° in 60 minutes
• Hour hand covers 360° in 12 hours
• The angle between hands depends on their relative positions

Example:
At 6:00, the hour hand is at 6 and the minute hand is at 12. The angle between them is 180°.

Importance in Quantitative Aptitude and Reasoning

Clock problems are a key part of quantitative aptitude for competitive exams because they test both calculation and logical thinking.

• Frequently asked in SSC, banking, MBA entrance, and defence exams
• Helps improve speed and accuracy in aptitude sections
• Based on fixed formulas and standard concepts, making them easy to master
• Questions can be solved quickly with practice

Because of their predictable nature, clock reasoning questions with answers are considered a high-scoring area for candidates who understand the basics well.

Basic Concepts of Clock Reasoning for Competitive Exams

Before applying formulas and shortcuts, it is important to understand the basic concepts of clock reasoning. A clear understanding of how a clock works helps in solving clock reasoning questions with answers, especially in exams like SSC, banking, MBA entrance, and defence exams. These concepts form the foundation for all clock aptitude problems, including angle-based and time-based questions.

Types of Angles in Clock Reasoning Questions (Acute, Obtuse, Straight)

In clock reasoning problems, many questions are based on identifying the type of angle formed between the hour and minute hands. Understanding these angle types is essential for solving clock angle questions in aptitude.

Acute Angle in Clock Reasoning

• An acute angle is less than 90°
• Example: At 2:00, the angle between the hands is 60°, which is acute
• Commonly asked in clock reasoning questions for SSC exams

Obtuse Angle in Clock Problems

• An obtuse angle is greater than 90° but less than 180°
• Example: At 5:00, the angle is 150°, which is obtuse
• Important for solving clock aptitude questions with angles

Straight Angle in Clock Reasoning

• A straight angle is exactly 180°
• Example: At 6:00, the hands form a straight line
• Frequently asked in clock reasoning questions for banking exams

Understanding these angle types helps in quickly identifying answers in multiple-choice clock reasoning questions.

Structure of a Clock in Reasoning (360 Degree Concept Explained)

To solve clock reasoning questions easily, you must understand the structure of a clock and how its hands move.

• A clock is a complete circle of 360°
• It is divided into 12 equal parts
• Each division represents 30°
• There are three hands: hour hand, minute hand, and second hand
• All hands move continuously, not in jumps

Key Angular Relationships in Clock Reasoning

• 12 hours = 360°
• 1 hour = 30°
• 60 minutes = 360° → 1 minute = 6° (for minute hand)
• Hour hand moves 30° in 60 minutes → 0.5° per minute
• 60 seconds = 360° → 1 second = 6°

These values are essential for solving clock reasoning formula-based questions.

Movement of Clock Hands and Angle Calculation Basics

Understanding the movement of clock hands is crucial for solving clock reasoning questions and answers:

• The minute hand moves faster and completes one full rotation in 60 minutes
• The hour hand moves slower and completes one full rotation in 12 hours
• The angle between the hands changes continuously with time
• The relative speed between hands helps in solving advanced problems

Example:
At 3:00, the minute hand is at 12 and the hour hand is at 3, forming a 90° angle.

Key Terms in Clock Reasoning You Must Know

To solve clock aptitude questions for competitive exams, you should be familiar with these important terms:

• Hour hand
• Minute hand
• Second hand
• Angle between hands
• Coinciding hands (overlapping positions)
• Opposite positions (180° apart)

These concepts are frequently used in clock reasoning questions with solutions.

Important Angle Values Table for Clock Reasoning

Here is a quick reference table for commonly used values in clock reasoning formulas and problems:

Types of Questions Based on Clock Reasoning

The types of questions asked about the clock are as follows -

1. Angle Between the hands of a clock

2. Defective Clock

3. Image-Based Questions

Let’s understand all of the types of clock-based questions with the help of the examples -

1. Angle Between the Hands of a Clock

In this type of question, we need to determine the angle between the hour hand and the minute hand of a clock for a specific time. To tackle these types of questions, we must have the basic knowledge of the angles traced by different hands of the clock. To find the angle between the hands of a clock, we can use the following clock reasoning angle formula.

The angle between the hands of a clock = (30 × Hours) − (5.5 × Minutes)

Example: Determine the angle between the hour and minute hands of the clock at 7:30.

By using the above formula, here, hours = 7 and minutes = 30

So, Angle = (30 × 7) − (5.5 × 30) = 210 − 165 = 45°

In this type, the reverse case is also possible, i.e., to find the time when the angle is known. For this, we have another clock reasoning formula.

Time = 211 [(Hours × 30) ± Angle]

If the time is between the first half (12 to 6), then the sign will be + (plus), and if the time is in between the second half (6 to 12), then the sign will be - (minus).

Example: At what time between 3 and 4 o’clock, the hands make an angle of 10°.

Here, both 3 and 4 lie in the first half, so consider the + sign.

Time = 211 [(3 × 30) + 10] = 211 [90 + 10] = 211 × 100 = 18211

So, the hands of the clock will make an angle of 10° at exactly 3 o’clock 18 minutes 10.9 seconds or 18211minutes past 3 o’clock.

2. Defective Clock

In this type, there is a comparison of time between an accurate clock and a defective clock. The defective clock indicates that the time in the clock is either slow or fast compared to the actual time. The wrong time can either be fast or delayed by a few seconds/minutes/hours or a few days/weeks. Let’s understand the concept with the help of an example.

Example: A watch gained 10 seconds in 5 minutes and was set right at 11 AM. What time will it show at 11 PM on the same day?

The watch gains 10 seconds in 5 minutes. So, in 60 minutes or 1 hour, it will gain 120 seconds. From 11 AM to 11 PM, the total time is 12 hours.

Thus, in 12 hours, it will gain 1440 seconds or 24 minutes.

So, when the actual time is 11 PM, the watch will show 11:24 PM.

3. Image-Based Clock Questions

In this type, the problems will be based on a clock’s mirror image or water image. These questions can be solved by either using the figures that show the mirror or the water image as directed in the question or by the formula. But out of the two methods, the best method is to use the formula.

a) Mirror Image-Based

When the time is given in 12-hour clock format, directly the formula that is given below.

Time in mirror image = 11:60 - Original Time

When the time is given in 24-hour clock format, the first step is to convert the time to 12-hour clock format and then use the above formula.

Example: If it is 3:50 in the clock, then what will be the time in the mirror?

Time in mirror image = 11:60 - Original Time = 11:60 - 3:50 = 8:10

Example: If it is 15:50 on the clock, then what will be the time in the mirror?

First, convert 15:50 to 12-hour clock format, the time will be 3:50

b) Water Image-Based

Time in water image = 18:30 - Original Time (when the minute is less than 30)

Time in water image = 17:90 - Original Time (when the minute is more than 30)

Example: If it is 2:40 on the clock, then what will be the time in the water?

Time in water image = 17:90 - Original Time = 17:90 - 2:40 = 15:50

The time will be 15:50 or 3 hours 50 minutes.

Verbal Reasoning Topics

Verbal reasoning is a core part of logical reasoning where questions are framed in words, statements, and numbers to test a candidate’s analytical and problem-solving ability. It checks how well you can interpret given information, draw conclusions, and apply reasoning skills in real-time scenarios. This section is highly important for SSC, Banking, Railway, CAT, UPSC, and other competitive exams. Below are the major verbal reasoning topics you should practice for exam success.

Clock Reasoning Questions for the Angle Between the Hands of a Clock

Q1. What will be the angle between two needles of a clock at 5:15?

A) 60°

B) 67.5° (correct)

C) 69°

D) 75°

Solution:
Given:
Hours = 5 and Minutes = 15

The angle between the hands of a clock = (30 × Hours) − (5.5 × Minutes)

So, Angle = (30 × 5) − (5.5 × 15) = 150 − 82.5 = 67.5°
Therefore, the angle between the hour hand and the minute hand at 5:15 is 67.5°. Hence, the second option is correct.

Q2. What will be the angle between the hour hand and the minute hand, if the clock shows 11:30?

A) 175°

B) 165° (correct)

C) 150°

D) 120°

Solution:
Given:
Hours = 11 and Minutes = 30

The angle between the hands of a clock = (30 × Hours) − (5.5 × Minutes)

So, Angle = (30 × 11) − (5.5 × 30) = 330 − 165 = 165°
Therefore, the angle between the hour hand and the minute hand at 11:30 is 165°. Hence, the second option is correct.

Q3. What will be the angle between the hour hand and the minute hand, if the clock shows 16:30?

A) 125°

B) 300°

C) 225°

D) 315°

Solution:
Given:
Hours = 16 and Minutes = 30

The angle between the hands of a clock = (30 × Hours) − (5.5 × Minutes)

So, Angle = (30 × 16) − (5.5 × 30) = 480 − 165 = 315°
Therefore, the angle between the hour hand and the minute hand at 16:30 is 315°. Hence, the fourth option is correct.

Q4. At what time between 4 and 5 o’clock, the hands make an angle of 45°.

A) 4:30

B) 3:30 (Correct)

C) 3:15

D) 3:45

Solution:

To calculate the time when the angle is given, use the following formula.

Time = 211 [(Hours × 30) ± Angle]

Here, both 4 and 5 lie in the first half, so consider the + sign.

Time = 211 [(4 × 30) + 45] = 211 [120 + 45] = 211 × 165 = 30

So, the hands of the clock will make an angle of 45° at exactly, 3:30. Hence, the second option is correct.

Q5. At what time between 9 and 10 o’clock, the hands make an angle of 50°.

A) 9:40 (Correct)

B) 9:20

C) 10:45

D) 9:50

Solution:

To calculate the time when the angle is given, use the following formula.

Time = 211 [(Hours × 30) ± Angle]

Here, both 9 and 10 lie in the second half, so consider the (-) sign.

Time = 211 [(9 × 30) - 50] = 211 [270 - 50] = 211 × 220 = 40

So, the hands of the clock will make an angle of 50° at exactly, 9:40. Hence, the first option is correct.

Clock Reasoning Questions for Defective Clock

Q1. A watch gained 5 seconds in 3 minutes and was set right at 9 AM. What time will it show at 9 PM on the same day?

A) 9:50

B) 10:20

C) 8:40

D) 9:20 (Correct)

Solution: The watch gains 5 seconds in 3 minutes. So, in 60 minutes or 1 hour, it will gain 100 seconds.

From 9 AM to 9 PM, the total time is 12 hours.

Thus, in 12 hours, it will gain 1200 seconds or 20 minutes.

So, when the actual time is 9 PM, the watch will show 9:20 PM. Hence, the fourth option is correct.

Q2. The clock was set on Monday at 5 AM. If the clock gains 30 minutes per hour, then what will be the time that the clock shows on Wednesday, 5 PM?

A) 11 PM, Friday

B) 11 PM, Thursday

C) 11 AM, Friday (Correct)

D) 11:30 PM, Thursday

Solution: The clock was set on Monday at 5 AM.

So, from Monday, 5 AM to Wednesday, 5 PM, the total time is 60 hours. Now, according to the given statement, the clock gains 30 minutes per hour. So, in total, the clock will gain 1800 minutes or 30 hours.

So, the clock will show the time 5 PM + 30 hours = 11 PM of Thursday on Wednesday, 5 PM.

Hence, the third option is correct.

Q3. An office has two wall clocks, one in the meeting room and the other in the boss’s cabin. The time displayed on both the clocks is 12 AM right now. The clock in the cabin gains 5 minutes every hour, whereas the one in the meeting room is slower by 5 minutes every hour. When will both the watches show at the same time again?

A) 72 hours (Correct)

B) 70 hours

C) 48 hours

D) 24 hours

Solution: The faster clock runs 5 minutes faster in 1 hour, and the slower clock runs 5 minutes slower in 1 hour.

Therefore, in 1 hour, the faster clock will trace 5 + 5 = 10 minutes more when compared to the slower clock. The following table shows the time difference between both the clocks.

From the above table, it is clear that in 6 hours, the faster clock will trace 60 minutes more when compared to the slower clock.

In 72 hours, the faster clock determines 12 hours more than the slower clock. At this point, both the clocks will show the same time, i.e., both the clocks will show the same time after exactly 72 hours.

Hence, the first option is correct.

Q4. The clock was set at 10 AM. If the clock gains 2 minutes per hour, then what will be the time that the clock shows at 11 PM on the same day?

A) 10:06 PM

B) 11:06 PM

C) 10:26 PM

D) 11:26 PM (Correct)

Solution: The watch gains 2 minutes per hour.

From 10 AM to 11 PM, the total time is 13 hours.

Thus, in 13 hours, it will gain 26 minutes.

So, when the actual time is 11 PM, the watch will show 11:26 PM. Hence, the fourth option is correct.

Q5. The clock was set at 1 PM. If the clock loses 30 seconds for every 5 minutes, then what will be the time that the clock shows at 9 PM on the same day?

A) 10:48 PM

B) 10:00 PM

C) 8: 48 PM

D) 9:48 PM (Correct)

Solution: The watch loses 30 seconds in 5 minutes. So, in 60 minutes or 1 hour, it will lose 360 seconds.

From 1 PM to 9 PM, the total time is 8 hours.

Thus, in 8 hours, it will lose 2880 seconds or 48 minutes.

So, when the actual time is 9 PM, the watch will show 9:48 PM. Hence, the fourth option is correct.

Best Books and Resources for Clock Reasoning Preparation

Here is a well-structured table of the most recommended books and resources to master clock reasoning questions, formulas, and tricks for competitive exams:

Clock Reasoning Questions for Image-Based Clock Questions

Q1. A clock shows 3:10 hours. What will be the time if it is seen in the mirror?

A) 6:10

B) 5:20

C) 8:50 (Correct)

D) 3:10

Solution: Time in mirror image = 11:60 - Original Time = 11:60 - 3:10 = 8:50

Hence, the third option is correct.

Q2. A clock shows 18:20 hours. What will be the time if it is seen in the mirror?

A) 4:40

B) 5:40 (Correct)

C) 8:10

D) 5:25

Solution: Time given = 18:20, since the given time is in 24-hour clock format. So, convert it to a 12-hour clock format. So, 18:20 → 6:20

Time in mirror image = 11:60 - Original Time = 11:60 - 6:20 = 5:40

Hence, the second option is correct.

Q3. A clock shows 5:10 hours. What will be the time if it is seen in the water?

A) 9:10

B) 5:20

C) 1:20 (Correct)

D) 3:10

Solution: Given time = 5:10
Since the minute is less than 30

Time in water image = 18:30 - Original Time = 18:30 - 5:10 = 13:20 or 1:20

Hence, the third option is correct.

Q4. If the water image of the clock shows 3:25, then what will be the actual time?

A) 3:25 (Correct)

B) 2:25

C) 5:50

D) 10:10

Solution: Since the minute is less than 30

Original Time = 18:30 - Time in water image = 18:30 - 3:25 = 15:05 or 3:25

Hence, the first option is correct.

Q5. If the mirror image of the clock shows 10:20, then what will be the actual time?

A) 7:50

B) 1:40 (Correct)

C) 6:20

D) 10:40

Solution: Original Time = 11:60 - Time in mirror image = 11:60 - 10:20 = 01:40

Hence, the second option is correct.

Step-by-Step Method to Solve Clock Problems (Easy and Accurate Approach)

Solving clock reasoning questions for competitive exams becomes much easier when you follow a structured method. This step-by-step approach helps improve both accuracy and speed in clock aptitude problems.

Understand the Question Type in Clock Reasoning

The first step is to identify what the question is asking:

• Angle between hands
• Time when hands coincide or are opposite
• Finding exact time for a given angle
• Mirror or incorrect clock problems

Recognizing the type helps you choose the correct clock formula and method instantly.

Apply the Correct Clock Formula

Once the question type is clear, apply the appropriate formula:

• Angle questions → use $|30H - 5.5M|$
• Time-based questions → use relative speed formulas
• Coinciding or opposite → use standard time intervals

Using the right formula is crucial for solving clock reasoning questions quickly and accurately.

Convert Time into Minutes if Needed

Many clock aptitude questions become easier when time is converted into minutes:

• Convert hours into minutes for consistency
• Example: 3:20 → 3 hours and 20 minutes
• Helps in applying formulas smoothly

This step is especially useful in advanced clock reasoning problems.

Calculate Angle or Time

Now perform the actual calculation:

• Substitute values in the formula
• Solve step-by-step carefully
• Keep track of units (degrees or minutes)

Example:
At 3:20 → Angle = $|30 \times 3 - 5.5 \times 20| = |90 - 110| = 20°$

Verify the Final Answer

Always double-check your answer:

• Ensure the angle is within 0° to 360°
• Check if the result matches the question condition
• Avoid calculation mistakes

Verification helps in avoiding errors in clock reasoning questions in exams.

Shortcut Tricks to Solve Clock Questions Quickly

Using smart shortcuts can significantly improve your performance in clock reasoning questions for SSC, banking, and MBA exams.

Direct Angle Calculation Trick

Instead of long steps, directly apply:

• Formula: $|30H - 5.5M|$
• Quickly substitute values without breaking into parts

This is the fastest way to solve clock angle problems.

Relative Speed Shortcut in Clock Problems

Understand the speed difference between hands:

• Minute hand = 6° per minute
• Hour hand = 0.5° per minute
• Relative speed = 5.5° per minute

This shortcut is useful for solving time and angle-based clock questions.

Standard Time Values to Remember

Memorizing common values saves time:

• Hands coincide every $65 \frac{5}{11}$ minutes
• Opposite positions occur 11 times in 12 hours
• Right angles occur 22 times in 12 hours

These are frequently used in clock reasoning previous year questions.

Elimination Technique for Clock MCQs

In multiple-choice questions:

• Eliminate clearly incorrect options
• Use approximation to narrow choices
• Focus only on logically possible answers

This technique improves speed in objective clock reasoning questions.

Approximation Method in Clock Problems

For faster solving:

• Estimate rough values instead of exact calculation
• Useful when options are far apart
• Helps save time in lengthy questions

This is especially helpful in time-bound competitive exams.

By following this step-by-step approach and applying these shortcut tricks, you can solve clock reasoning questions with formulas quickly, accurately, and confidently.

Clock Reasoning Questions for CAT/ APICET/ JIPMAT

Generally, 1 question of clock reasoning in the CAT exam and 2-3 questions in APICET and JIPMAT are seen in the exam.

Q1. The time in a clock is 20 minutes past 2. Find the angle between the hands of the clock.

1. 60 degrees

2. 120 degrees

3. 45 degrees

4. 50 degrees

Solution:

Angle =11/2m-30h

⇒ Angle = 11x 20/2 – 30 x 2= 110 -60 = 50

Hence, the fourth option is correct.

Q2. A clock loses 1% time during the first week and then gains 2% time during the next week. If the clock was set right at 12 noon on a Sunday, what would be the time that the clock would show exactly 14 days from when it was set right?[CAT 2016]

1. 1: 36: 48

2. 1: 40: 48

3. 1: 41: 24

4. 10: 19: 12

Solution:

One week has 7 * 24 = 168 hours.

If the clock loses 1% time during the first week, then it will show a time of 1% less than 168 hours = 1.68 hours less.

Subsequently, in the second week, it gains 3.36 hours more than the actual time.

As it lost 1.68 hours during the first week and then gained 3.36 hours the next week, the net gain = 1.68 hours.

So the clock will show a time which is 1.68 hours more than 12 Noon two weeks after the given time.

1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds.

i.e. 1: 40: 48 P.M. Hence, the second option is correct.

Clock Reasoning Questions for VITEEE/ CUET

Generally, 1-2 questions of the clock have been seen in the VITEEE and CUET exams.

Q-1) Directions: The image of a clock in a mirror is seen as 3:15. What is the right time?

1) 8:45

2) 10:45

3) 7:45

4) 9:45

Hint: Subtract the reflected time from 11:60 to get the actual time.

Solution:

Because the time 3:15 lies between 1:00 and 11:00, so to get the actual time subtract the reflected time from 11:60.

Actual time = 11:60 – 3:15 = 8:45

So, 8:45 is the right time. Hence, the first option is correct.

Important Clock Formulas and Rules (Quick Revision Table)

Below is the table with short tricks for clock reasoning, which will be helpful for quick revision, speed and solving:

Common Mistakes to Avoid in Clock Reasoning

Even after learning the clock reasoning formulas and tricks, many candidates lose marks because of small errors. Understanding these common mistakes in clock reasoning questions can help students avoid confusion and solve problems with accuracy in exams like SSC, Banking, Railways, and CAT.

Misinterpreting AM and PM in Questions

One of the most frequent errors is misreading the time format in clock reasoning questions. Many aptitude tests give time in AM/PM format, but candidates often assume it is always a 12-hour format. This mistake can lead to wrong answers in angle between clock hands questions or overlapping problems. Always check whether the clock is shown in 12-hour or 24-hour format before solving.

Forgetting to Apply the Correct Formula

Another common error is forgetting or misusing the clock reasoning formula. Candidates sometimes calculate the angle between hour and minute hands using basic subtraction instead of applying the formula:

Angle = |(30 × Hour) – (11/2 × Minutes)|

Skipping this step or using incorrect substitution can easily result in errors, especially in clock reasoning aptitude tests where time is limited. Regular practice with clock reasoning mock test helps in avoiding such mistakes.

Confusing Mirror Image and Water Image Problems

Mirror image and water image questions in clock reasoning often confuse candidates. In mirror image of a clock, the reflection appears as if viewed in a mirror placed vertically, while in water image, the reflection is flipped as if seen on water below. Many students interchange these concepts and lose marks in mirror image clock reasoning questions for SSC exams. Practicing with examples of both types ensures clarity during the exam.

Non Verbal Reasoning Topics

Non-verbal reasoning is an important part of logical reasoning where problems are solved using diagrams, shapes, and figures instead of words or numbers. It tests a candidate’s ability to analyze patterns, visualize changes, and apply logic without relying on language skills. This section plays a vital role in exams like SSC, Banking, Railway, CAT, and other aptitude tests. Below are the major non-verbal reasoning topics you need to prepare for competitive exams.