Clock – Fast watch (gains 10 min/day): A clock is set right at 10:00 am. It gains 10 minutes in 24 hours. What is the true time when the watch indicates 3:00 pm the next day?

Introduction / Context:
Fast/slow clock problems compare indicated (watch) time to true time based on a constant daily gain or loss. Here, the watch gains 10 minutes per day.

Given Data / Assumptions:

• Set correct at t=10:00 am (Day 1).
• Gain = +10 minutes per 24 hours.
• Indicated time later: 3:00 pm (Day 2), i.e., 29 hours indicated after 10:00 am previous day.

Concept / Approach:
Relate indicated time to true time via a rate factor. If a watch shows 24 h 10 m when 24 h have truly passed, the rate factor is (24 h + 10 m) / 24 h = 145/144.

Step-by-Step Solution:
1) Indicated elapsed = 29 h (from 10:00 am Day 1 to 3:00 pm Day 2).2) True elapsed = indicated / (145/144) = 29 * 144/145 = 28.8 h = 28 h 48 m.3) Add to 10:00 am Day 1 → True time = Day 2 at 2:48 pm.

Verification / Alternative check:
Proportion method: gain 10 m per 24 h means ~0.4167 m per hour. Over 28 h 48 m true, watch gains about 12 m (rounding aligns to indicated 29 h).

Why Other Options Are Wrong:
2:12 pm, 2:30 pm, 2:45 pm → do not match the computed 2:48 pm true time.

Common Pitfalls:
Subtracting 10 minutes directly from the indicated time or forgetting that gain accumulates proportionally with elapsed true time.

Final Answer:
48 min past 2 pm