A clock is set right at 5:00 am and loses 16 minutes in every 24 hours. What is the true time when this slow clock indicates 10:00 pm on the 4th day?

Introduction / Context:
A slow clock shows less indicated time than true. Convert indicated elapsed time to true elapsed using the rate factor for loss.

Given Data / Assumptions:

• Loss: 16 min per 24 h → rate r = indicated/true = (1440 − 16)/1440 = 1424/1440.
• Set right: 5:00 am (Day 1).
• Indicated: 10:00 pm on Day 4.

Concept / Approach:
Indicated elapsed from Day 1 5:00 am to Day 4 10:00 pm = 3 days 17 h = 89 h. True elapsed = 89 * (1440/1424) = 90 h.

Step-by-Step Solution:
Add 90 h to 5:00 am (Day 1) → Day 4 11:00 pm.

Verification / Alternative check:
Since the clock is slow, true time should be later than indicated; 11:00 pm is 1 hour later than 10:00 pm, consistent with the computed factor.

Why Other Options Are Wrong:
9:00 am/pm and 11:00 am violate direction (they imply earlier time), not later.

Common Pitfalls:
Using inverse factor (making the time earlier instead of later).

Final Answer:
11 : 00 pm