Clock Hand Overlap & Opposite Practice Questions

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Clock Hand Overlap & Opposite Notes – Examples

A. Overlap (Hands coincide – 0°)

Formula: Time after H o’clock = 60 × H / 11 minutes

B. Opposite (Hands at 180°)

Formula: Time after H o’clock = 60 × H ± 180/11 minute

1. Between 1 and 2 o’clock

T = 60 × 1 / 11 = 5.45 min ≈1:05:45

2. Between 2 and 3 o’clock

T = 60 × 2/11 = 0.18 min ≈ 2:11:30

3. When do the hands overlap after 3 o’clock?

Time = 60×3/11=180/11 ≈ 16 minutes 36 seconds

Ans: 3:16:36

4. When do the hands overlap after 7 o’clock?

Time = 60×7/11= 420/11 ≈ 38 minutes 18 seconds

Ans: 7:38:18

5. When do the hands overlap after 10 o’clock?

Time = 60×10/11= 600/11 ≈ 54 minutes 55 seconds

Ans: 10:54:55

Tip for Learners:

• Always remember the formula Time = 60H / 11


• H = starting hour


• The fraction part is minutes in decimal fraction


• Convert fraction into seconds if needed for exact time

B. Opposite (Hands at 180°)

Formula: Time after H o’clock = 60 × H ± 180/11 minutes

1.     Between 1 and 2 o’clock

T₁ = 60×1−180/11 = −120/11 → ignore negative

T₂ = 60×1+180/11 = 240/11 = 21.21 min ≈ 1:22:21

2.     Between 2 and 3 o’clock

T₁ = 60×2−180/11 = 60/11= 5.45 min ≈ 2:05:54

T2 = 60×2+180/11 = 300/11 = 27.27 min ≈ 2:27:27

3. When are the hands opposite after 2 o’clock?

Time = 60×2+180/11 = 300/11 ≈ 27 minutes 27 seconds

Also using minus:

Time =120−180/11= −60/11 (ignore negative, consider previous hour)

Ans: 2:27:27

4. When are the hands opposite after 5 o’clock?

Time = 60×5−180/11=120/11 ≈ 11 minutes 30 seconds

Ans: 5:11:30

5. When are the hands opposite after 8 o’clock ?

Time = 60×8+180/11= 660/11 = 60 minutes = 9:00

Ans: 9:00

Clock Hand Overlap Practice

Find Time : Formula Reminder:- Time after H o’clock = 60 × H / 11 minutes, (H = hour)

1. Between 1 and 2 o’clock

Time = 60×1 / 11 = 60/11 = 5.45 min, Ans: 1: 05.54

2. Between 2 and 3 o’clock

Time = 60×2 / 11 = 120/11 = 11.30 min, Ans: 2:11:30

3. Between 3 and 4 o’clock

Time = 60×3 / 11 = 180/11 =  16.36 min, Ans: 3:16:36

4. Between 4 and 5 o’clock

Time = 60×4 / 11 = 240/11 = 22.21 min, Ans: 4:22.21

5. Between 5 and 6 o’clock

Time = 60×5 / 11 = 300/11 = 27.27 min, Ans: 5:27:27

6. Between 6 and 7 o’clock

Time = 60×6 / 11 = 360/11 = 33:12 min, Ans: 6:33:12

7. Between 7 and 8 o’clock

Time = 60×7 / 11 = 420/11 = 38:18 min, Ans: 7:38:18

8. Between 8 and 9 o’clock

Time = 60×8 / 11 = 480/11 = 44:03 min, Ans: 8:44:03

9. Between 9 and 10 o’clock

Time = 60×9 / 11 = 540/11 = 49:09 min, Ans: 9:49:09

10. Between 10 and 11 o’clock

Time = 60×10 / 11 = 600/11 = 54:54 min, Ans: 10:54:54