Clock – General Aptitude for GATE, PSU, ESE, AE/JE | Priyanka Ma’am

Clock is an important topic in General Aptitude and is frequently asked in GATE, PSU, ESE, AE/JE exams. It tests your understanding of angles, speed, and time relationships.

Basic Concepts

A clock has two main hands:

• Minute Hand
• Hour Hand

Both move at different speeds and form angles at different times.

Important Facts

• Clock has 360°
• 12 hours → 360° → 1 hour = 30°
• 1 minute → 6°
• Minute hand speed = 6°/min
• Hour hand speed = 0.5°/min

Key Formulas

• Angle = |30 × H − 5.5 × M|
• Relative Speed = 5.5° per minute

Types of Questions

• Angle between hands
• Time when hands coincide
• Time when hands are opposite
• Mirror clock questions

Solved Examples

Example 1

Find angle at 3:00.

Angle = 30 × 3 = 90°

Example 2

Find angle at 4:20.

Angle = |30×4 − 5.5×20| = |120 − 110| = 10°

Example 3

How many times do hands coincide in 12 hours?

11 times

Example 4

At what time between 2 and 3 will hands be at 90°?

Use formula: 30H − 5.5M = 90
60 − 5.5M = 90 → M ≈ 10.91 min
Time ≈ 2:10:55

Shortcut Tricks

• Remember 30° per hour
• Use formula directly for angle
• Coincidence every 65 5/11 minutes
• Opposite every 32 8/11 minutes

Questions

Q1. Find angle at 6:00.

= 180°

Q2. Find angle at 9:15.

= |270 − 82.5| = 187.5° (or smaller angle = 172.5°)

Exam Tips

• Memorize angle formula
• Practice approximation
• Focus on smaller angle unless specified
• Practice previous year questions

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