Numerical aptitude · Calendars and clocks
Clocks, made easy
💡 The idea
The minute hand moves 6° a minute. The hour hand moves ½° a minute (30° an hour). So the minute hand gains 5½° every minute.
minute hand
6° a minute→hour hand
½° a minute→gap closes
5½° a minute
6° a minute→hour hand
½° a minute→gap closes
5½° a minute
🧭 The method: 3 steps
- Hour hand angle from 12 = 30 × hours + ½ × minutes.
- Minute hand angle from 12 = 6 × minutes.
- Angle between = the difference (if it is over 180°, use 360 − it). Meeting times: gap ÷ 5½.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. Angle at 3:40?
- Hour hand: 30 × 3 + 20 = 110°
- Minute hand: 6 × 40 = 240°
- Difference: 130°
⚡ Shortcut: |30H − 5½M| = |90 − 220| = 130.
Example 2. When do the hands meet between 2 and 3?
- At 2:00 the hour hand is 60° ahead
- Gain 5½° a minute: 60 ÷ 5½ = 10 10/11 min past 2
⚠️ Where people go wrong
- Forgetting that the hour hand moves between the numbers.
- The hands meet 22 times a day, not 24.
- Mirror: 11:60 − the time you see.
📌 Remember
- |30H − 5½M|
- Together: 11 times in 12 h
- Right angle: 44 times a day
- Mirror: 11:60 − time