Clock: Meaning, Reasoning Questions and Answers, Formula

What is Clock Reasoning?

Clock reasoning questions prompt you to figure the angle between the hour and minute hands, or to figure out the exact time when they coincide or end up opposite each other. Because they run on fixed formulas and patterns, clock reasoning is often treated as a high-scoring section in SSC, Banking, MBA entrance, Railway, and defence exams.

Basic Concepts of Clock Reasoning

• The minute hand moves 6° per minute.
• The hour hand moves 0.5° per minute.
• The angle between the hands changes continuously as they move.

Types of Angles

• Acute Angle: Less than 90°
• Obtuse Angle: Between 90° and 180°
• Straight Angle: Exactly 180°

Important Terms

• Hour hand
• Minute hand
• Angle between hands
• Coinciding hands
• Opposite hands

Important Clock Values

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

To find the angle between the hour and minute hands at a given time, use the standard clock angle formula based on the movement of both hands.

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 these questions, there is a defective clock that runs either fast or slow versus the actual time. You’ll need to compare the times that are given , so you can figure out the correct time or the clock’s rate. Let’s take it step by step.

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. Questions Based on Images of a Clock

These questions are about getting the mirror image, or the water reflection of a clock time, and most people solve them quickly using the usual formula, even when it feels a bit odd at first.

a) Mirror image based

If the time is already shown in a 12 hour clock, then just use the formula straight away, it is written below.

Time in mirror image = 11:60 - Original Time

But if the time is given in 24 hour clock format then the first thing you have to do is convert it into 12-hour clock format, ok then apply the same formula, as above.

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 about how you analyze the statements, interpret the information, then reach logical conclusions.

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’s a list of some of the top books for getting good at clock reasoning, formulas, quick tricks and also plenty of practice questions, 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 way to figure out Clock Problems fast

Use these steps so clock reasoning questions feel manageable, and also more accurate, especially if time is tight.

First, figure out what question you got

Decide if it’s:

• Angle between the hands
• Hands that meet, or they are opposite
• Finding the exact time when an angle is given
• Mirror clock stuff , or faulty clock variations

Then, use the right formula (don’t mix them up)

Pick the formula that matches the exact type you identified

• For angle questions
• For time-based ones

For coinciding, or opposite hands problems

Next, do the actual calculation

Put in the values carefully, solve, and don’t forget the unit you’re supposed to end up with (either degrees , or minutes)

Finally, verify it

Make sure your result actually fits the condition, and that it matches what the question is asking for in the end.

Quick shortcut ideas for clock questions

• For angle based questions, use the direct angle idea first.
• Keep in mind how the hour hand and minute hand move relative to each other.
• Try to memorize common positions too, when they coincide or when they are opposite.

If it’s MCQs, remove the wrong options quickly by using estimation plus logic, so you don’t waste time staring at everything.

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

Avoid these everyday mistakes to boost accuracy in clock reasoning queries: Misread AM and PM, or the given time presentation. Don’t use the wrong formula, or swap in incorrect numbers. Also, don’t ignore that the hour hand moves continuously, not in jumps. Be careful with mirror image vs water image clock problems they aren’t the same. Finally, always do a quick verification of the final answer before you lock in an option.

Non-Verbal Reasoning Topics

Non verbal reasoning, tests how well you spot patterns, forms, and the way visual relationships happen. Take a look at the key non verbal reasoning topics below , for your competitive exam preparation.