Clocks
Clocks
Clock problems involve finding angles between hands, determining when hands coincide or form right angles, and solving faulty-clock problems. The minute hand moves at 6°/minute and the hour hand at 0.5°/minute, giving a relative speed of 5.5°/minute.
Key Idea
Learn the angle formula |30H − 5.5M|. Apply it directly at any time. If result > 180, subtract from 360 to get the smaller angle. This one formula handles most clock MCQs.
Core Formulas
Angle formula
Angle = |30H − 5.5M| degrees (subtract from 360 if > 180)
To find angle between clock hands at time H:M
Relative speed
Minute hand gains 5.5° per minute over hour hand
Rate at which minute hand overtakes hour hand
Coincidence interval
Hands meet every 65(5/11) minutes = 720/11 minutes
Time between successive overlaps
Right angle times
Hands at 90° 22 times in 12 hours
Count of right angle positions
Faulty clock
Gain per hour × hours elapsed = total extra time shown
For fast/slow clock problems
Relevant Exams
1–2 questions per exam. Most common: find angle between hands at given time, find when hands coincide or are perpendicular. Angle formula solves 90% of clock questions.