Clock Reasoning : Aptitude Test

Angular Distance of Clock Hands


 Minute Hand : 360° in 60 minutes → 1 minute = 6°  


So, the movement of the minute hand = 6° × minutes


Ex: If the minute hand is at 40 minutes: Angle moved = 40 × 6 = 240°



    Hour Hand: 360° in 12 hours → 1 hour = 30°, Movement of hour hand per minute = 30° ÷ 60 = 0.5° per minute


Ex: At 8:45 → Hour hand angle = (8 × 30) + (45 × 0.5) = 240 + 22.5 = 262.5°


      Second Hand: 360° in 60 seconds → 1 second = 6°,  So, movement of the second hand = 6° × seconds


Ex: At 3:00 → Second hand angle = 0 × 6 = 0°


Notes / Relative Speeds


i.     Second hand moves 60 times faster than the minute hand.


ii.   Minute hand moves 12 times faster than the hour hand.


iii.   Second hand moves 720 times faster than the hour hand.


Examples:


1. A clock runs from 2:00 PM to 4:15 PM. How many degrees does the hour hand move during this time ?


Options: (a) 68.5° (b) 67.5° (c) 66.5° (d) 61°


Soln:



  • Time Duration = 2 hours 15 minutes = 135 minutes

  • Hour hand moves 0.5° per minute

  • Total movement = 135 × 0.5 = 67.5°


Ans: (b) 67.5°


2. A clock runs from 8:45 AM to 10:12 AM. How many degrees will the hour hand move during this time ?


Options: (a) 40.5° (b) 41.5° (c) 43.5° (d) 44°


Soln:



  • Time Duration = 8:45 AM to 10:12 AM = 1 hour 27 minutes = 87 minutes

  • Hour hand moves 0.5° per minute

  • Total movement = 87 × 0.5 = 43.5°


Answer: (c) 43.5°


3. At 3:00 PM, the hour hand moves 135°. What time will the clock show ?


Options: (a) 7:29 PM (b) 7:31 PM (c) 7:30 PM (d) 8:30 PM


Soln:



  • Hour hand moves 0.5° per minute, so 1° = 2 minutes

  • 135° = 135 × 2 = 270 minutes = 4 hours 30 minutes

  • Add to 3:00 PM → 3:00 + 4:30 = 7:30 PM


Ans: (c) 7:30 PM



4. A clock runs from 8:00 AM to 8:40 AM. How many degrees will the minute hand move during this time ?


Options: (a) 180° (b) 240° (c) 275° (d) 90°


        Soln:



  • Minute hand completes 360° in 60 minutes → 1 minute = 6°

  • Time Duration = 40 minutes

  • Total movement = 40 × 6 = 240°


Ans: (b) 240°


@@@. Clock Angle Shortcut for Time Ratio 1:10



  • Rule: When the time ratio is 1:10 (Hour : Minute), multiply the hour number by 25 to get the angle between the hands.


Ex:


Time = 8:40 AM



  1. The hour part = 8 → 25 × 8 = 200° (intermediate step)

  2. The minute part = 40 → 25 × 4 = 100° (final angle between hands)


Ans: 100°


This is a 


@@@. Clock Angle Shortcut for Time Ratio 1:5 or 1:6



  • Rule: When the time ratio is 1:5 or 1:6 (Hour : Minute), take half of the minute value to get the angle between the hour and minute hands.


Ex:


1.   Time = 8:40 : Minute = 40 → Half = 40 ÷ 2 = 20°


2.   Time = 7:35 : Minute = 35 → Half = 35 ÷ 2 = 17.5°


3.   Time = 4:24 : Minute = 24 → Half = 24 ÷ 2 = 12°


Summary:



  • Minute ÷ 2 = Angle between hands (for 1:5 or 1:6 ratios)

  • Very useful for quick calculations in exams without using the full formula.