Clocks
Angle between hands, time calculations
Clock problems are a common topic in aptitude tests that involve calculating angles between clock hands, determining times when hands are in specific positions (overlap, opposite, perpendicular), and solving problems related to fast or slow clocks. Understanding the movement rates of hour and minute hands is essential for solving these problems efficiently.
Key formulas and rules
Key concepts
Understanding Clock Hand Movements
The hour hand completes one full rotation (360 deg) in 12 hours, moving at 30 deg per hour or 0.5 deg per minute. The minute hand completes one full rotation in 60 minutes, moving at 6 deg per minute. The second hand moves at 6 deg per second. The relative speed between minute and hour hands is crucial - the minute hand gains 5.5 deg per minute over the hour hand.
Calculating Angle Between Hands
To find the angle at H hours M minutes, use the formula: |30H - 5.5M|. This gives the angle measured clockwise from the hour hand to the minute hand. If the result exceeds 180 deg, subtract it from 360 deg to get the smaller angle between the two hands. For example, at 3:40, the angle is |30x3 - 5.5x40| = |90 - 220| = 130 deg.