A watch is 3 minutes slow at 5:00 pm on Tuesday and 5 minutes fast at 11:00 pm on Wednesday. When did it show the correct time?

Introduction / Context:
A uniformly gaining watch goes from being slow to fast across an interval. The instant when the error is zero is the time it shows correctly.

Given Data / Assumptions:

• Error at start (Tue 5:00 pm) = -3 minutes.
• Error at end (Wed 11:00 pm) = +5 minutes.
• Elapsed real time = 30 hours.

Concept / Approach:
Assuming uniform rate change, the error changes linearly from -3 to +5, a span of 8 minutes. The watch is correct when cumulative change equals +3 minutes from the start error.

Step-by-Step Solution:
Total error change = +8 minutes over 30 hours.Time to cancel -3 minutes = (3/8)*30 hours = 11.25 hours.Add 11 hours 15 minutes to Tue 5:00 pm → Wed 4:15 am.

Verification / Alternative check:
From Wed 4:15 am to Wed 11:00 pm is 18 hours 45 minutes, during which error increases from 0 to +5, consistent with the uniform rate.

Why Other Options Are Wrong:
7:30 am corresponds to (2.5/8)*30 = 9.375 hours, not matching; Tuesday 3:45 pm is before the start observation.

Common Pitfalls:
Taking simple average of the two readings without time-weighting; confusing gain with error offset.

Final Answer:
Wednesday 4:15 am