Quick Concept Summary
Clock problems become much easier once you remember that the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute.
Worked Examples
Example 1
Find the angle at 3:30.
| ` | 30x3 - 5.5x30 | = | 90 - 165 | = 75 degrees` |
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Example 2
Find the smaller angle at 12:30.
| ` | 30x12 - 5.5x30 | = 195 degrees` |
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Smaller angle is 360 - 195 = 165 degrees.
Common Question Types
- Angle between hands
- Hands coincide
- Hands opposite each other
- Right-angle positions
- Fast or slow clocks
Practice Questions
1. Find the angle at 5:20. 2. How many times do the hands coincide in 12 hours? 3. A clock gains 5 minutes per hour. If set right at 8 AM, what will it show at noon?
Common Mistakes
- Treating the hour hand as stationary
- Forgetting to choose the smaller angle
- Mixing actual time with shown time in faulty-clock questions