An accurate clock is started at noon. By 10 minutes past 3, the hour hand has…
2025
An accurate clock is started at noon. By 10 minutes past 3, the hour hand has turned through:
- A.
90
- B.
95
- C.
100
- D.
105
Show answer & explanation
Correct answer: B
Concept: On a clock face, the hour hand completes one full 360° revolution in 12 hours (720 minutes), so it turns at a constant rate of 360/720 = 0.5° per minute (equivalently 30° per hour).
From noon (12:00) to 3:10, the elapsed time is 3 hours and 10 minutes, i.e. 3 × 60 + 10 = 190 minutes.
At 0.5° per minute, the hour hand turns through 190 × 0.5 = 95° in this time.
Cross-check: using the hour-hand position formula angle = 30 × H + 0.5 × M (H = completed hours, M = minutes past the hour), with H = 3 and M = 10: 30 × 3 + 0.5 × 10 = 90 + 5 = 95°, confirming the same result.
Answer: The hour hand has turned through 95°.