Clock Reasoning : Aptitude Test 1
1. At 7:30, what will be the angle between the hour and minute hands ?
Options: (a) 45° (b) 60° (c) 90° (d) 300°
Soln:
Minute hand at 30 min: 30 × 6° = 180°
Hour hand at 7:30:
· 7 hours → 7 × 30° = 210°
· Extra 30 min → 0.5° × 30 = 15°
· Total = 210° + 15° = 225°
Angle = |225° − 180°| = 45°
Ans: (a) 45°
2. What will be the angle between the hour and minute hands at 8:50 ?
Options: (a) 90° (b) 325° (c) 35° (d) Both (b) and (c)
Solution:
Use the formula: θ = ∣60H−11M∣ / 2
Here: H = 8, M = 50
Θ = ∣60×8−11×50∣ / 2
= ∣480 - 550∣ / 2
=70 / 2 = 35∘
· Small angle = 35°
· Large angle = 360° - 35° = 325°
Ans: (d) Both (b) and (c)
3. What is the angle between the hour and minute hands at 5:25 ?
Options: (a) 27.5° (b) 27° (c) 14.5° (d) 12.5°
Soln:
Use the same formula: θ = ∣60H-11M∣ / 2
H = 5, M = 25
Θ = ∣60×5 - 11×25∣ / 2
= ∣300 - 275∣ / 2
= 25 / 2 = 12.5∘
Ans: (d) 12.5°
4. Find the angle between the hour and minute hands at 3:12.
Options: (a) 25° (b) 24° (c) 12° (d) None of these
Soln :
Use the formula: θ = ∣60H−11M∣ / 2
Here: H = 3, M = 12
Θ = ∣60×3−11×12∣ / 2
= ∣180 - 132∣ / 2
= 48 / 2 = 24∘
So the angle is 24°.
Shortcut Trick:
When the hour : minute ratio = 1 : 4, → Just multiply the minutes by 2.
Here time = 3:12 (ratio 1:4)
= 12×2=24∘
Ans: (b) 24°
5. Find the angle between the hour and minute hands at 8:40.
Options: (a) 10° (b) 22.5° (c) 20° (d) 50°
Ans: (c) 20°
Soln :
At 8:40, the hour : minute ratio is 1 : 5.
For ratios 1:5 or 1:6, use this shortcut:
Angle = (Minutes ÷ 2)
40 ÷ 2 = 20∘
So, the angle = 20°
Alternate Formula Method:
Use the standard formula: θ = ∣60H−11M∣ / 2
H = 8
M = 40
Θ = ∣60 × 8−11 × 40∣ / 2
= ∣480 - 440∣ / 2
=40 / 2 = 20∘
Ans: (c) 20°
6. Find the angle between the hour and minute hands at 8:40.
Options: (a) 10° (b) 22.5° (c) 20° (d) 50°
Ans: (c) 20°
Soln :
At 8:40, the hour : minute ratio is 1 : 5.
For ratios 1:5 or 1:6, use this shortcut:
Angle = (Minutes ÷ 2)
40 ÷ 2 = 20∘
So, the angle = 20°
Alternate Formula Method:
Use the standard formula: θ = ∣60H−11M∣ / 2
H = 8
M = 40
Θ = ∣60 × 8−11 × 40∣ / 2
= ∣480 - 440∣ / 2
=40 / 2 = 20∘
Ans: (c) 20°