Two clocks are set right at 10:00 am. One gains 20 seconds per 24 hours; the other loses 40 seconds per 24 hours. When the gaining clock indicates 4:00 pm on the following day, what is the true time?

Introduction / Context:
Only the gaining clock's rate matters here because we are told its indicated time. Convert its indicated elapsed time back to true elapsed time using the rate factor.

Given Data / Assumptions:

• Gaining clock: +20 s per 24 h → rate r = (86400+20)/86400 = 86420/86400.
• Indicated elapsed: 10:00 am (Day 1) → 4:00 pm (Day 2) = 30 h.

Concept / Approach:
True elapsed = indicated / r = 30 h * (86400/86420) = 30 * (4320/4321) h.

Step-by-Step Solution:
True elapsed ≈ 29 h 59 m 35 s.Add to 10:00 am → next day ≈ 3:59:35 pm.

Verification / Alternative check:
Since the clock is slightly fast, true time must be a little earlier than 4:00 pm; 3:59:35 pm is consistent.

Why Other Options Are Wrong:
Other values either round incorrectly or assume the losing clock’s rate (irrelevant here).

Common Pitfalls:
Using the reverse factor (making time later, not earlier).

Final Answer:
3 : 59 : 35 pm (next day)