Clock questions in OPSC ASO are mostly mirror times (ASO 2018 and 2021) and the angle between the hands. Both are formula questions.
Speeds of the hands
- Minute hand: 6° per minute. Hour hand: 0.5° per minute (30° per hour).
- The minute hand gains 5.5° per minute on the hour hand.
Angle between the hands
Angle = |30H − 5.5M|. If the result is more than 180°, subtract it from 360°. At 3:40: |90 − 220| = 130°.
Mirror time
Mirror time = 11:60 − actual time. 8:40 → 3:20; 6:07 → 5:53 (ASO 2018); 3:15 → 8:45 (ASO 2021). The rule works in both directions, so the same formula gives the real time from a mirror reading.
When the hands coincide
Between H and H + 1 o'clock, the hands meet 60H/11 minutes past H. In a day they coincide 22 times, are at right angles 44 times, and are in a straight line 44 times.
Fast and slow clocks
Use simple proportion: a clock that gains g minutes in 24 hours gains g × (hours ÷ 24) minutes.