CLOCK – Reasoning Notes (CUET | CLAT | IPMAT)

CLOCK – Reasoning Notes (CUET | CLAT | IPMAT | SSC | BANKING)

Clock questions test your understanding of angles, relative speed, mirror–image logic, time gain/loss, and position of hands in an analogue clock.

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1. BASIC CONCEPTS

1.1 Movement of Clock Hands

Hand	Movement	Speed
Hour hand	360° in 12 hours	0.5° per minute
Minute hand	360° in 60 minutes	6° per minute

1.2 Relative Speed

Minute hand speed – Hour hand speed
= 6° – 0.5° = 5.5° per minute

This is the relative speed used for:

• Meeting of hands

• Overlapping

• Angle-based problems

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TYPE 1: ANGLE BETWEEN CLOCK HANDS

Formula

Angle =       | 30H - 5.5M |

Where H = hour, M = minute.

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Example 1 (CUET )

Q. Find the angle between the hands at 5:40.

Solution:
Using formula:   |30H - 5.5M|
                           |30(5) - 5.5(40)|
                           |150 - 220| = 70°

Answer: 70°

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Example 2 (CLAT )

Q. What is the angle between the hands at 7:20?

Solution:
|30(7) - 5.5(20)| = |210 - 110| = 100°

Answer: 100°

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TYPE 2: WHEN DO THE HANDS MEET? (OVERLAP):

Minute and hour hands overlap every 65 5/11 minutes.

General Formula

Time after H o’clock when hands meet:                (H x 60 ) / 11     minutes

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Example 3 (SSC)

Q. When will the hands meet after 4 o’clock?

         (4 x 60) / 11   = 240/11

Answer: 21 9/11 minutes past 4

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TYPE 3: WHEN DO THE HANDS FORM A RIGHT ANGLE (90°)

Minute and hour hands are 90° apart twice every hour.

Formula

| 30H - 5.5M | = 90

Solve for M.

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Example 4 (IPMAT PYQ-Type)

Q. At what time after 3 o’clock will the hands be at 90°?

|90 - 5.5M| = 90

Case 1:

90 - 5.5M = 90                                          M = 0

Case 2:

90 - 5.5M = -90

-5.5M = -180

M = 32.72

Answer: 3:32:43 minutes approx.

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TYPE 4: WHEN ARE THE HANDS OPPOSITE (180° APART)?

Formula

| 30H - 5.5M | = 180

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Example 5 (CUET PYQ-type)

Q. Find the time when the hands are opposite after 8 o’clock.

|240 - 5.5M| = 180

Solving:

240 - 5.5M = 180

5.5M = 60

M = 10.9

Answer: 8:10:54 minutes

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TYPE 5: HANDS AT 0° (OVERLAP), 90°, AND 180° IN GENERAL

List of standard values

Type	Time interval
Overlap	65 5/11 min
90°	32 8/11 min after every hour (twice)
180°	49 1/11 min after every hour

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TYPE 6: TIME GAIN/LOSS BY A SLOW OR FAST CLOCK

Formula

Gain or Loss per day = Difference in time shown

Actual time = Given time  / Rate factor 

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Example 6

Q. A clock gains 5 minutes in 24 hours. If it shows 7 PM now, what is the real time?

Clock runs 1440 min → shows 1445 min
Rate = 1445/1440

Actual time when clock shows 7 hours =

{420} / {1445/1440} = 418.5 

= 6 : 58.5 PM

Answer: 6:58:30 PM

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TYPE 7: CLOCK MIRROR QUESTIONS

Mirror Time Formula (Vertical Mirror)

Mirror Image Time = 11:60 

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Example 7 (CLAT PYQ-Type)

Q. A clock shows 3:25. What will be its mirror image?

11:60 - 8:50 = 3:10

Answer: 8:35

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Example 8 (CUET PYQ-Type)

Q. What is the mirror image of 8:50?

11:60 - 8:50 = 3:10

Answer: 3:10

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TYPE 8: CLOCK HANDS EXCHANGE THEIR POSITIONS

Minute and hour hands exchange positions when:

| 30(H+1) - 5.5M | = | 30H - 5.5(60-M) |

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Example 9 (IPMAT PYQ-Type)

Q. At what time between 1 and 2 do the hands exchange positions?

Solving standard result:

Time = {(H x 60) + 180} / {11}

For H = 1:
                                     { 60 + 180}/{11} = 240/ 11 = 21.81

Answer: 1:21:49

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TYPE 9: HOW MANY TIMES DO THE HANDS MEET, 90°, 180° IN 12 HOURS?

Event	Frequency in 12 Hours
Overlap	11 times
Right angle	22 times
Opposite	11 times

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Example 10 (SSC)

Q. How many times are the hands opposite in 24 hours?

11 times in 12 hrs → 22 times in 24 hrs

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TYPE 10: SHORTEST DISTANCE BETWEEN HANDS

Formula

Angle = |30H - 5.5M|

Shortest distance =
If angle > 180° → 360° – angle
Else → angle

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Example 11 (CUET )

Q. Find the smallest angle between hands at 9:20.

|30(9) - 5.5(20)| = |270 - 110| = 160°

Since 160 < 180 → 160°

Answer: 160°

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TYPE 11: SPECIAL QUESTIONS (TRICKY)

Example 12 (Bank PO PYQ-Type)

Q. A clock strikes once at 1 o’clock, twice at 2 o’clock, and so on.
How many times will it strike in 24 hours?

Strikes in 12 hours:

1+2+3+…+12 = 78

In 24 hours:
78 x 2 = 156

Answer: 156

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HIGH-LEVEL SUMMARY FORMULAS

1. Angle Formula

|30H - 5.5M|

2. Meeting Time

Hx60 /11

3. Mirror Image

11:60 - Actual Time

4. Opposite Hands

|30H - 5.5M| = 180

5. 90° Hands

|30H - 5.5M| = 90