Clock Puzzles with Answers Practice for Interviews, Online Test and Competitive Exams.
Q1. What is the time when the minute hand and hour hand are at the same position after 3:00?
Correct Answer:
16 minutes past 3
Explanation: For the hour and minute hands to be in the same position after 3:00, the minute hand must catch up with the hour hand.
Relative speeds: The minute hand moves at 6° per minute.
The hour hand moves at 0.5° per minute.
The minute hand gains 6° - 0.5° = 5.5° per minute.
Initial angle difference at 3:00:
At 3:00, the hour hand is at 90° (3 × 30°), and the minute hand is at 0°. So, the difference is 90°.
Time to catch up:
To close the 90° gap at a rate of 5.5° per minute:
Time = 90° ÷ 5.5° ≈ 16 4/11 minutes.
Thus, the hour and minute hands overlap 16 4/11 minutes past 3:00.
The correct answer is 16 minutes past 3.
Q2. If the hour hand is at 5 and the minute hand is at 12, what is the angle between them?
Correct Answer:
150°
Explanation: At 5:00, the hour hand is at 5 × 30° = 150° from the 12th hour mark.
The minute hand is at the 12th mark, 0° from 12.
The angle between them is 150° - 0° = 150°.
Q3. How much time does the minute hand take to overtake the hour hand?
Correct Answer:
65 5/11 minutes
Explanation: The minute hand overtakes the hour hand every 65 5/11 minutes. To explain why, consider the following: The minute hand moves 360° in 60 minutes, so it moves at a rate of 6° per minute.
The hour hand moves 30° in one hour (or 0.5° per minute).
The minute hand gains 5.5° per minute (6° - 0.5°).
To overtake the hour hand, the minute hand needs to catch up the 360° difference (one full revolution).
So, the time it takes for the minute hand to overtake the hour hand is:
360°/5.5° = 65 * 5 / 11 minutes
=65 * 5/11 minutes Therefore, the correct answer is b) 65 5/11 minutes.
Q4. What is the angle between the hour hand and the minute hand at 4:40?
Correct Answer:
100°
Explanation: The minute hand is at the 8th mark (40 minutes), so it is 240° from 12.
The hour hand at 4:00 is at 120° (4 × 30°). In 40 minutes, the hour hand moves 0.5° per minute × 40 = 20°.
The hour hand will be at 120° + 20° = 140°.
The angle between the two is 240° - 140° = 100°.
Q5. What is the angle between the hour hand and the minute hand at 2:25?
Correct Answer:
77.5°
Explanation: The minute hand is at the 5th mark (25 minutes), so it is 150° from 12.
The hour hand at 2:00 starts at 60° (2 × 30°). In 25 minutes, the hour hand moves 0.5° per minute × 25 = 12.5°.
So, the hour hand will be at 60° + 12.5° = 72.5°.
The angle between the two is 150° - 72.5° = 77.5°.
Q6. At 12:00, what is the angle between the hour hand and the minute hand?
Correct Answer:
0°
Explanation: At 12:00, both the hour hand and the minute hand overlap exactly at the 12th hour, forming a 0° angle. So, the answer is 0°.
Q7. If the angle between the hour and minute hands is 90° at a certain time, what is the possible time?
Correct Answer:
All of the above
Explanation: When the angle between the hour and minute hands is 90°, it can occur at multiple times:
3:00: The hour and minute hands are 90° apart.
6:00: The angle is 180° between the hands, but the minute hand moves to 12.
9:00: The hour and minute hands form a right angle (90°).
Q8. What is the angle between the hour hand and the minute hand at 6:00?
Correct Answer:
180°
Explanation: At 6:00, the hour hand is exactly at the 6th hour mark (180°) and the minute hand is at 12, which is 0°. The angle between them is 180°. So, the answer is 180°.
Q9. The time is 8:20. What is the angle between the hour hand and the minute hand?
Correct Answer:
50°
Explanation: The minute hand at 20 minutes is at 120°.
The hour hand at 8:00 starts at 240° (8 × 30°) and moves further because 20 minutes is 1/3 of an hour. In 20 minutes, the hour hand moves 0.5° × 20 = 10°.
So, the hour hand will be at 240° + 10° = 250°.
The angle between the minute hand and the hour hand is 250° - 120° = 130°.
Q10. What is the angle between the hour hand and the minute hand at 3:15?
Correct Answer:
7.5°
Explanation: At 3:15, the hour hand is a quarter past 3, so it's 1/4th of the way from 3 to 4. The minute hand at 15 minutes is at the 3rd mark.
The hour hand moves 0.5° per minute (30° per hour).
In 15 minutes, the hour hand moves 0.5 × 15 = 7.5°.
The minute hand at 15 minutes is 90° from the 12th hour mark.
The angle between the two is 90° - 7.5° = 82.5°.
Q11. What is the reflex angle between the hands of a clock at 6:45?
Correct Answer:
292.5°
Explanation: Smaller angle:
360° − (|Hour Angle − Minute Angle|) For 6:45, calcuation as follows: Hour angle:
The hour hand is at 6:00 (6 × 30° = 180°).
For the 45 minutes, it moves 45 × 0.5° = 22.5°.
So, the hour angle is 180° + 22.5° = 202.5°.
Minute angle:
The minute hand is at 45 minutes (45 × 6° = 270°).
Angle between them:
|202.5° − 270°| = 67.5°.
Smaller angle:
360° − 67.5° = 292.5°.
So, the smaller angle between the hour and minute hands at 6:45 is 292.5°.
Q12. How many times in a day do the hands of a clock coincide?
Correct Answer:
12
Explanation: The hands coincide once every hour, making it 12 times in a 24-hour period.
Q13. What is the smaller angle formed by the hands of a clock at 10:30?
Correct Answer:
90°
Explanation: Hour hand:
10 × 30 + 30 × 0.5 = 315°.
The hour hand is at 315°.
Minute hand:
30 × 6 = 180°.
The minute hand is at 180°.
Angle:
|315 - 180| = 135°.
The angle between the hands is 135°.
Smaller angle:
360 - 135 = 90°.
The smaller angle between the hour and minute hands is 90°.
Q14. At what time between 11:00 and 12:00 will the hands of the clock be perpendicular?
Correct Answer:
11:38
Explanation: The equation for a right angle between the hour and minute hands is:
|30H - (11M / 2)| = 90.
1. When H = 11 (for 11 o'clock), substitute H into the equation:
|30 × 11 - (11M / 2)| = 90.
This simplifies to:
|330 - (11M / 2)| = 90.
2. Now, solve for M by considering two cases:
- Case 1: 330 - (11M / 2) = 90.
- Case 2: 330 - (11M / 2) = -90.
3. Solving for M in both cases gives us M ≈ 38.18, which is about 38 minutes.
So, when H = 11, the time is 11:38.
Q15. How many times in a day do the hands of a clock form an acute angle?
Correct Answer:
72
Explanation: Acute angles occur twice every hour.
In 24 hours, the total number of acute angles is calculated as:
24 × 3 = 72. So, there are 72 acute angles in 24 hours.