Clock Puzzles with Answers Practice for Interviews, Online Test and Competitive Exams.
Q16. At 8:20, what is the angle between the hour and the minute hands?
Correct Answer:
130°
Explanation: Hour hand:
The hour hand moves 30° per hour, so at 8:00, it is at 8 × 30° = 240°.
Additionally, for 20 minutes, it moves 20 × 0.5° = 10°.
Total position of the hour hand: 240° + 10° = 250°.
Minute hand:
The minute hand moves 6° per minute, so at 20 minutes, it is at 20 × 6° = 120°.
Angle between them:
The absolute difference is |250° - 120°| = 130°.
So, the angle between the hour and minute hands is 130°.
Q17. At what time between 9:00 and 10:00 do the hands of the clock form a straight line?
Correct Answer:
9:45
Explanation: For a straight line between the hour and minute hands, the equation is:|30H - (11M / 2)| = 180. When H = 9 (for 9 o'clock), substitute H into the equation: |30 × 9 - (11M / 2)| = 180, which simplifies to: |270 - (11M / 2)| = 180. Solve for M: First, we consider two cases:
Case 1: 270 - (11M / 2) = 180.
Case 2: 270 - (11M / 2) = -180.
In both cases, solving for M gives us M = 45 minutes. So, when the hour hand is at 9, the minute hand is at 45 minutes. The time is 9:45.
Q18. If a clock runs 10 minutes fast every hour, what will be the time shown on the clock 6 hours after it is set correctly at 12:00?
Correct Answer:
7:00
Explanation: In 6 hours, the clock gains 6 × 10 = 60 minutes. This means that after 6 hours, the clock will be ahead by 60 minutes, or 1 hour. If the actual time is 6:00, the clock will show 7:00.
Q19. What is the time between 2:00 and 3:00 when the hands of the clock are perpendicular?
Correct Answer:
2:27
Explanation: The equation for a right angle between the hour and minute hands is:|30H - (11M / 2)| = 90. When H = 2 (for 2 o'clock), the equation becomes: |30 × 2 - (11M / 2)| = 90, which simplifies to: |60 - (11M / 2)| = 90. Solving for M, we get: 11M / 2 = 60 - 90 = -30, or 11M / 2 = 60 + 90 = 150. From these, M = 27.27, which is approximately 27 minutes. So, the time when the hands form a right angle is 2:27.
Q20. If the clock reads 6:40, what is the angle between the hour and minute hands?
Correct Answer:
100°
Explanation: Hour hand: At 6:40, the hour hand starts at 6 × 30° = 180° and moves 40 × 0.5° = 20° for the 40 minutes. So, it’s at 180° + 20° = 200°.
Minute hand: The minute hand moves 6° per minute, so at 40 minutes, it’s at 40 × 6° = 240°.
Angle between them: The absolute difference is |200° - 240°| = 40°.
Q21. How many times a day do the hands of a clock form a straight line?
Correct Answer:
44
Explanation: Hands form a straight line twice every hour (0° and 180°). For 24 hours: 24 * 2 = 44.
Q22. At what time do the hands of a clock overlap between 7:00 and 8:00?
Correct Answer:
7:37
Explanation: Equation: 30H - (11M/2) = 0. Solving for H = 7, M = 37.09 ≈ 37 minutes.
Q23. What is the reflex angle between the hands of a clock at 3:15?
Correct Answer:
270°
Explanation: The smaller angle is 90°. Reflex angle = 360° - 90° = 270°.
Q24. A clock is set at 12:00. If it gains 2 minutes every hour, what will be the time after 6 hours?
Correct Answer:
6:12
Explanation: In 6 hours, the clock gains 6 * 2 = 12 minutes. The time = 6:12.
Q25. At what time between 4:00 and 5:00 will the hands of a clock coincide?
Correct Answer:
4:20
Explanation: For coincidence, 30H - (11M/2) = 0. Solving for H = 4, M = 21.8 ≈ 21 minutes.
Q26. If a clock is 5 minutes slow every hour, how much time will it lose in a day?
Correct Answer:
2 hours 20 minutes
Explanation: In 24 hours, the clock loses 24 * 5 = 120 minutes, i.e., 2 hours 20 minutes.
Q27. How many times in a day do the hands of a clock form a right angle?
Correct Answer:
96
Explanation: A clock forms right angles twice every hour (90° and 270°). For 24 hours: 24 * 4 = 96.
Q28. At what time between 1:00 and 2:00 will the hands of the clock be opposite to each other?
Correct Answer:
1:32
Explanation: For opposite hands, the angle is 180°. Equation: 30H - (11M/2) = 180. Solving for H = 1, M = 32.7 ≈ 32 minutes.
Q29. The time on a clock is 10:10. What is the angle between the hour and the minute hands?
Correct Answer:
115°
Explanation: At 10:10, the minute hand is at 60 degrees (10 minutes * 6°/minute), and the hour hand is at 305° (10 hours * 30° + 10 minutes * 0.5°). The angle = |305° - 60°| = 115°.