Clock
Clock problems are a common topic in quantitative aptitude involving angles between hour and minute hands. These questions test logical thinking and are frequently asked in competitive exams.
Fundamental Principles
Minute Hand Speed
The minute hand moves 360° in 60 minutes → 6° per minute.
Hour Hand Speed
The hour hand moves 360° in 12 hours → 30° per hour or 0.5° per minute.
Angle Formula
Angle = |30H − 5.5M| degrees, where H = hour and M = minutes.
Essential Formulation Tips
- Always take absolute value of angle.
- Use formula directly instead of drawing diagrams.
- Remember minute hand moves faster than hour hand.
- Convert time into minutes if needed.
Shortcut Execution Techniques
- Angle = |30H − 5.5M|.
- For 90° → |30H − 5.5M| = 90.
- For 180° → |30H − 5.5M| = 180.
- Coincidence occurs when angle = 0°.
Contextual Inquiries (FAQs)
Q: What is the fastest way to solve clock problems?
A:
Q: When do clock hands coincide?
A:
Example Breakdown: Basic Angle Example
Basic concept.Use formula: |30H − 5.5M|.
H = 3, M = 0.
Angle = |30×3 − 0| = 90°.
Final Answer: 90°.
Example Breakdown: General Time Example
Common exam question.H = 4, M = 20.
Angle = |30×4 − 5.5×20|.
= |120 − 110| = 10°.
Final Answer: 10°.
Example Breakdown: Right Angle Example
Important pattern.Use formula: |30H − 5.5M| = 90.
H = 2 → |60 − 5.5M| = 90.
Solve → 5.5M = 150 → M ≈ 27.27.
Time ≈ 2:27.
Final Answer: approx 2:27.
Clock Practice Questions
Solve important clock aptitude questions for banking, SSC, CMAT, and placement exams.
Q1. Find angle at 6:00.
Q2. Find angle at 9:00.
Q3. At what time do hands coincide between 1 and 2?