Clocks
Clocks
Find angles between clock hands, determine when they coincide or form right angles, and solve faulty-clock problems. The minute hand gains 5.5\u00B0 per minute over the hour hand. SSC and RRB papers test 1\u20132 clock questions per exam \u2014 the single angle formula |30H \u2212 5.5M| handles 90% of them.
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)
Plug in hours H and minutes M to get the angle instantly \u2014 subtract from 360 if the result exceeds 180
Relative speed
Minute hand gains 5.5° per minute over hour hand
Use this rate to calculate how long until the hands reach a target angle from their current position
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.