NMAT LRDI Clocks: Formulas, Concepts, Shortcuts & Preparation

Clock questions require you to understand how the hour and minute hands move relative to each other. They can involve finding the angle between hands, identifying overlap, calculating right or straight angles, or determining the effect of a clock gaining or losing time.

Since NMAT is a speed-based exam, understanding the NMAT exam pattern can help you plan time for calculation-heavy questions. PW supports NMAT preparation with learning resources that can be used alongside regular practice to build familiarity with these question types. 

Basic Movement of Clock Hands

A clock completes one full revolution of 360° in 12 hours. Therefore, the hour hand and minute hand move at different rates.

The hour hand continues moving as the minutes pass. Therefore, it should not be treated as fixed at a particular hour mark.

Angle Between Hour and Minute Hands

The standard formula for finding the angle between the hour and minute hands is:

θ = |30H − 11M/2|

Where:

• H = hour

• M = minutes

• θ = angle between the hands

The absolute value ensures that the calculated angle is positive.

Example: Angle at 4:20

θ = |30(4) − 11(20)/2|

θ = |120 − 110|

θ = 10°

This formula is generally the safest method for standard angle questions.

Reflex Angle Between Clock Hands

The reflex angle is the larger angle formed by the two hands.

If the smaller angle is θ:

Reflex angle = 360° − θ

For example, if the smaller angle is 142.5°:

Reflex angle = 360° − 142.5° = 217.5°

Therefore, read the wording carefully. If the question specifically asks for the reflex angle, use the larger angle rather than the smaller one.

Quick Shortcut for Special Times

Some clock times follow a useful pattern:

• 1:05

• 2:10

• 3:15

• 4:20

• 5:25

• 6:30

• 7:35

• 8:40

• 9:45

• 10:50

• 11:55

For these times, the angle can be identified using: M/2

For example, at 4:20: 20/2 = 10°

So, the angle between the hands is 10°.

However, use this shortcut only when the given time fits the pattern. For other times, the standard angle formula is more reliable.

Finding the Rotation of the Hour Hand

If the question asks only for the rotation of the hour hand, use:

Hour-hand movement = 30H + M/2

For example, at 4:10: 30(4) + 10/2 = 120 + 5 = 125°

Do not use the angle-between-hands formula when the question asks specifically for the movement of the hour hand.

Clockwise and Anticlockwise Movement

Clockwise movement means moving forward in time, while anticlockwise movement means moving backwards.

For example, if a clock shows 10:30 and the minute hand moves 12 minutes clockwise, the new time becomes:

10:30 + 12 minutes = 10:42

The required angle can then be calculated using the standard formula.

Understanding “Past” and “To”

Clock questions often use phrases that can cause confusion if they are not converted into standard time.

Always convert such statements into digital time before applying a formula.

When Do the Clock Hands Overlap?

The hands overlap when both occupy the same position.

Therefore: Angle = 0°

Using the angle equation: 30H = 11M/2

So: M = 60H/11

For example, between 4 and 5:

M = 60(4)/11

M = 240/11 = 21 9/11 minutes

Therefore, the hands overlap at approximately 4:21 9/11.

Number of Overlaps

The hands overlap:

• 11 times in 12 hours

• 22 times in 24 hours

They do not overlap exactly at every hour because the hour hand keeps moving while the minute hand completes its rotations.

Converting Fractional Minutes into Seconds

Clock questions may give answers in fractional minutes.

To convert the fractional part into seconds:

Fractional minute × 60 = seconds

For example: 9/11 × 60 = 540/11 seconds = 49 1/11 seconds

This conversion is useful when the answer needs to be expressed in minutes and seconds.

When Are the Hands Exactly Opposite?

When the hands are exactly opposite each other, the angle between them is: 180°

Therefore: |30H − 11M/2| = 180°

Since the equation contains an absolute value, consider the appropriate case while solving.

A straight-line position of the hands also represents a 180° angle.

When Do the Hands Form a Right Angle?

A right angle occurs when the hands are 90° apart.

Therefore: |30H − 11M/2| = 90°

There can be more than one right-angle position within a given hour interval. Therefore, check both possible configurations when the question asks for all possible times.

Important Clock Positions

Clock Gain and Loss Questions

Some clock questions involve a clock that gains or loses time compared with the actual time.

Clock Gains Time

If a clock gains 5 minutes every hour:

• After 1 hour → 5 minutes gained

• After 2 hours → 10 minutes gained

• After 6 hours → 30 minutes gained

Therefore, if the correct time is 6:00, the fast clock will show: 6:30

The basic rule is: Gain → Add the extra time

Clock Loses Time

If a clock loses time, subtract the lost duration from the actual time.

Loss → Subtract the lost time

Finding Gain Per Hour

Sometimes the gain or loss per hour is not directly provided.

You may be given:

• The time when the clock was correct

• A later reference time

• The incorrect time displayed by the clock

First find the difference between the actual elapsed time and the time shown by the clock. Then divide the total gain or loss by the number of elapsed hours.

Example

Suppose a clock shows 7:35 when the actual elapsed time is 7 hours.

Total gain = 35 minutes

Gain per hour: 35 ÷ 7 = 5 minutes per hour

This method can then be applied to longer durations.

How to Prepare NMAT LRDI Clocks

A useful NMAT preparation strategy should combine formula revision with timed practice. Focus on understanding the movement of both hands rather than memorising isolated answers.

1. Learn the Core Formulas

Be comfortable with: θ = |30H − 11M/2|, Hour-hand movement = 30H + M/2, and Minute-hand movement = 6M. Also remember the equations for 0°, 90° and 180° positions.

2. Practise Different Question Types

Do not restrict practice to angle-based questions. Include:

• Overlap questions

• Right-angle questions

• Opposite-hand questions

• Reflex-angle questions

• Clockwise and anticlockwise movement

• Gain and loss questions

• “Past” and “to” time expressions

3. Use Shortcuts Carefully

Recognise special time patterns where a shortcut can save calculation time. However, use the standard formula whenever the pattern does not clearly apply.

4. Work on Calculation Accuracy

Fractions such as 180/11, 240/11 and 540/11 can appear in clock questions. Practise handling these values without making avoidable calculation errors.

5. Practise NMAT PYQs

Solving NMAT PYQs can help you become familiar with the way clock concepts are framed and identify which calculations you can perform quickly. After solving, analyse the method rather than checking only whether the final answer is correct.

6. Use Timed Practice

Include clock questions while taking an NMAT mock test so that you can judge whether a question is worth solving immediately or should be revisited later.

Final Preparation Checklist for NMAT LRDI Clocks

Before the NMAT exam, make sure you can quickly:

• Calculate the angle between clock hands

• Find a reflex angle

• Calculate hour-hand rotation

• Identify overlap times

• Solve opposite-hand questions

• Solve right-angle questions

• Handle clockwise and anticlockwise movement

• Convert “past” and “to” expressions into standard time

• Solve clock gain and loss questions

• Convert fractional minutes into seconds

• Apply shortcuts without compromising accuracy

NMAT LRDI Clocks becomes easier when you are comfortable with hand movement, angle formulas and common clock positions. Focus on solving different question types accurately, recognising useful shortcuts and managing calculation time during practice. 

PW supports NMAT preparation with learning resources that can be used alongside regular LRDI practice to improve familiarity with clock-based and other logical reasoning questions.