📑 Topics on this page (Jump to Topic):
📌 1. Basic Facts
| Hand | Speed |
|---|---|
| Minute hand | 6° per minute |
| Hour hand | 0.5° per minute (30° per hour) |
| Relative speed | 5.5° per minute |
- Angle = |30H − 5.5M|; if over 180°, subtract from 360°.
- 12 numbers, 30° between each; every minute mark is 6°.
📌 2. Hand Positions (in 12 hours)
| Position | In 12 h | In 24 h |
|---|---|---|
| Coincide (0°) | 11 | 22 |
| Opposite (180°) | 11 | 22 |
| Right angle (90°) | 22 | 44 |
| Straight line (0° or 180°) | 22 | 44 |
- Hands coincide between H and H+1 at M = (60/11) × H minutes past H.
- Hands meet every 65 5/11 minutes; if they meet every 65 minutes the clock gains time.
⚠️ Exam Traps:
- At both 3:00 and 9:00 the angle is 90°; at 6:00 it is 180°; at 12:00 it is 0°.
- Between 5 and 6 the hands are never opposite (that happens exactly at 6:00); between 11 and 1 they meet only at 12:00 — hence 11, not 12, times in 12 hours.
📌 3. Mirror Image of a Clock
- Mirror time = 11:60 − given time (for times between 1:00 and 11:00).
- Around 12 o'clock use 23:60 − time.
- Water-image time = 18:30 − given time (adjust by 12 if needed).
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. Angle between the hands at 3:00? Practice
Correct answer: (B)
|30×3 − 0| = 90°.
|30×3 − 0| = 90°.
Q2. Angle between the hands at 4:20? Practice
Correct answer: (C)
|120 − 5.5×20| = |120 − 110| = 10°.
|120 − 5.5×20| = |120 − 110| = 10°.
Q3. Angle between the hands at 7:30? Practice
Correct answer: (D)
|210 − 165| = 45°.
|210 − 165| = 45°.
Q4. How many times do the hands coincide in 12 hours? Practice
Correct answer: (A)
11 times in 12 hours (they meet at 12 once, not separately between 11 and 1).
11 times in 12 hours (they meet at 12 once, not separately between 11 and 1).
Q5. How many times are the hands at right angles in a day (24 hours)? Practice
Correct answer: (B)
22 times in 12 hours ⇒ 44 in 24 hours.
22 times in 12 hours ⇒ 44 in 24 hours.
Q6. At what time between 2 and 3 o'clock will the hands coincide? Practice
Correct answer: (C)
M = (60/11) × 2 = 120/11 = 10 10/11 min.
M = (60/11) × 2 = 120/11 = 10 10/11 min.
Q7. A clock shows 8:20. What time does its mirror image show? Practice
Correct answer: (D)
11:60 − 8:20 = 3:40.
11:60 − 8:20 = 3:40.
Q8. How many degrees does the hour hand turn from 9:00 to 9:30? Practice
Correct answer: (A)
30 min × 0.5° = 15°.
30 min × 0.5° = 15°.
Q9. Angle between the hands at 6:00? Practice
Correct answer: (B)
|180 − 0| = 180°.
|180 − 0| = 180°.
Q10. Smaller angle between the hands at 10:10? Practice
Correct answer: (C)
|300 − 55| = 245° ⇒ smaller angle 360 − 245 = 115°.
|300 − 55| = 245° ⇒ smaller angle 360 − 245 = 115°.
Q11. A clock gains 2 minutes every hour. It is set right at 6 a.m. What will it show at 12 noon (true time) the same day? Practice
Correct answer: (D)
6 hours × 2 min = 12 min fast ⇒ 12:12.
6 hours × 2 min = 12 min fast ⇒ 12:12.
Q12. Angle between the hands at 2:30? Practice
Correct answer: (A)
|60 − 165| = 105°.
|60 − 165| = 105°.
Q13. A clock shows 2:45. What does the mirror image show? Practice
Correct answer: (B)
11:60 − 2:45 = 9:15.
11:60 − 2:45 = 9:15.
Q14. How many degrees does the minute hand turn in 15 minutes? Practice
Correct answer: (C)
15 × 6° = 90°.
15 × 6° = 90°.
Q15. At what time between 4 and 5 are the hands opposite (180°)? Practice
Correct answer: (D)
5.5M − 120 = 180 ⇒ M = 300/5.5 = 600/11 = 54 6/11 min. (At 21 9/11 they coincide, not oppose.)
5.5M − 120 = 180 ⇒ M = 300/5.5 = 600/11 = 54 6/11 min. (At 21 9/11 they coincide, not oppose.)
Q16. Angle between the hands at 3:15? Practice
Correct answer: (A)
|90 − 82.5| = 7.5°.
|90 − 82.5| = 7.5°.
Q17. A clock loses 3 minutes every hour. How far behind will it be after 8 hours? Practice
Correct answer: (B)
8 × 3 = 24 min.
8 × 3 = 24 min.
Q18. At 9:00, what is the clockwise angle from 12 to the hour hand? Practice
Correct answer: (C)
9 × 30° = 270° (the smaller angle is 90°).
9 × 30° = 270° (the smaller angle is 90°).
Q19. A clock shows 11:10. What is the mirror-image time? Practice
Correct answer: (D)
11:60 − 11:10 = 0:50 = 12:50.
11:60 − 11:10 = 0:50 = 12:50.
Q20. Angle between the hands at 1:00? Practice
Correct answer: (A)
|30 − 0| = 30°.
|30 − 0| = 30°.