Aptitude Topics
Clock Basics
A clock is a circle (360°) divided into 12 hour spaces. Each hour space represents 30° ($360/12$). The minute hand travels 360° in 60 minutes, while the hour hand travels 360° in 12 hours.
Fundamental Principles
Angular Speed of Minute Hand
The minute hand moves 360° in 60 minutes, meaning it covers 6° per minute.
Angular Speed of Hour Hand
The hour hand moves 30° in 60 minutes (the space of one hour), meaning it covers 0.5° per minute.
Essential Formulation Tips
- The relative speed between the minute and hour hands is $6^{\circ} - 0.5^{\circ} = 5.5^{\circ}$ per minute.
- Use the 12 o'clock position as your 0° reference point for all calculations.
Shortcut Execution Techniques
- To find the position of the hour hand at any time (H:M), use the formula: $\theta = 30H + 0.5M$.
Example Breakdown: Angular Movement
Problem QueryHow many degrees does the minute hand move in 20 minutes?
Step-By-Step Solution Path
Speed = 6° per minute.
Distance = $20 \text{ minutes} \times 6^{\circ}/\text{min} = 120^{\circ}$.
Speed Calculations
Practice finding how far hands move over specific intervals.
Q1. How many degrees does the hour hand move in 30 minutes?