Clock
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Solved Examples
Study MaterialSolved Examples – Clock
Solved examples help students understand the practical application of clock concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, Defence, and other aptitude examinations.
Topics Covered in Solved Examples
- Angle Between Clock Hands
- Coinciding Hands Problems
- Right Angle Problems
- Opposite Hands Questions
- Mirror Image Questions
- Fast and Slow Clock Problems
- Clock Hand Movement Concepts
- Advanced Clock Aptitude Questions
Example 1: Finding Angle Between Clock Hands
Question: Find the angle between the hour hand and minute hand at 3:20.
Solution:
Using formula:
Angle = |30h − 11m/2|
= |30 × 3 − 11 × 20/2|
= |90 − 110|
= 20°
Therefore:
Angle = 20°
Example 2: Right Angle Problem
Question: What is the angle between the hands of a clock at 9:00?
Solution:
At 9:00:
- Minute hand points at 12.
- Hour hand points at 9.
Difference:
= 3 divisions
Angle:
= 3 × 30°
= 90°
Therefore:
Angle = 90°
Example 3: Straight Angle Problem
Question: Find the angle between the hands at 6:00.
Solution:
At 6:00:
- Minute hand is at 12.
- Hour hand is at 6.
Difference:
= 6 divisions
Angle:
= 6 × 30°
= 180°
Therefore:
Angle = 180°
Example 4: Angle at 4:30
Question: Find the angle between the hands at 4:30.
Solution:
Using formula:
Angle = |30h − 11m/2|
= |30 × 4 − 11 × 30/2|
= |120 − 165|
= 45°
Therefore:
Angle = 45°
Example 5: Coinciding Hands
Question: How many times do the hands of a clock coincide in 12 hours?
Solution:
Important fact:
Clock hands coincide:
= 11 times in 12 hours
Therefore:
Answer = 11 times
Example 6: Right Angle Frequency
Question: How many times do the hands of a clock form right angles in 12 hours?
Solution:
Important fact:
Clock hands form right angles:
= 22 times in 12 hours
Therefore:
Answer = 22 times
Example 7: Smaller Angle Problem
Question: Find the smaller angle between the hands at 8:20.
Solution:
Using formula:
Angle = |30 × 8 − 11 × 20/2|
= |240 − 110|
= 130°
Since 130° < 180°:
Smaller angle = 130°
Therefore:
Smaller Angle = 130°
Example 8: Reflex Angle Problem
Question: Find the reflex angle between the hands at 5:20.
Solution:
Angle:
= |30 × 5 − 11 × 20/2|
= |150 − 110|
= 40°
Reflex angle:
= 360° − 40°
= 320°
Therefore:
Reflex Angle = 320°
Example 9: Mirror Image Problem
Question: Find the mirror image of 7:25.
Solution:
Mirror Time:
= 11:60 − 7:25
= 4:35
Therefore:
Mirror Image = 4:35
Example 10: Standard Position Problem
Question: What is the angle between the hands at 12:00?
Solution:
At 12:00:
- Both hands overlap.
Therefore:
Angle = 0°
Answer = 0°
Example 11: Advanced Angle Problem
Question: Find the angle between the hands at 2:45.
Solution:
Using formula:
Angle = |30 × 2 − 11 × 45/2|
= |60 − 247.5|
= 187.5°
Smaller angle:
= 360° − 187.5°
= 172.5°
Therefore:
Smaller Angle = 172.5°
Example 12: Opposite Hands Problem
Question: How many times do the hands of a clock become opposite in a day?
Solution:
Hands become opposite:
= 11 times in 12 hours
Therefore:
= 22 times in 24 hours
Answer = 22 times
Example 13: Fast Clock Problem
Question: A clock gains 5 minutes every hour. How much time will it gain in 24 hours?
Solution:
Gain per hour:
= 5 minutes
Gain in 24 hours:
= 24 × 5
= 120 minutes
= 2 hours
Therefore:
Clock gains 2 hours
Example 14: Slow Clock Problem
Question: A clock loses 3 minutes every hour. How much time will it lose in 10 hours?
Solution:
Loss per hour:
= 3 minutes
Loss in 10 hours:
= 10 × 3
= 30 minutes
Therefore:
Clock loses 30 minutes
Example 15: Minute Hand Movement
Question: How many degrees does the minute hand cover in 15 minutes?
Solution:
Minute hand speed:
= 6° per minute
In 15 minutes:
= 15 × 6°
= 90°
Therefore:
Angle covered = 90°
Example 16: Hour Hand Movement
Question: How many degrees does the hour hand move in 2 hours?
Solution:
Hour hand movement per hour:
= 30°
In 2 hours:
= 2 × 30°
= 60°
Therefore:
Angle covered = 60°
Important Exam Tips
- Memorize all important formulas.
- Use the direct angle formula carefully.
- Remember hour hand moves continuously.
- Use smaller angle unless specified.
- Practice mirror image problems regularly.
- Draw rough diagrams for complex problems.
- Verify calculations carefully.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving clock questions in competitive examinations.