Run-fast watch, every 30 min it gains 3 min: After setting correct time at 5:00 am, what time will the watch show after 6 hours?

Introduction / Context:
“Gains 3 minutes every 30 minutes” means the watch runs 10% fast relative to real time: in 30 real minutes, it shows 33 minutes. Scaling proportionally finds the shown reading after a given real-time interval.

Given Data / Assumptions:

• Real elapsed time = 6 hours = 360 minutes.
• Watch runs 10% fast: shown time = real time × 1.1.

Concept / Approach:
Compute the shown minutes and add to the start time (5:00 am).

Step-by-Step Solution:

Verification / Alternative check:
Chunking 6 hours as twelve 30-minute blocks: each gains 3 minutes ⇒ 12 × 3 = 36 minutes extra; 6:00 real becomes 6:36 shown.

Why Other Options Are Wrong:
10:54/11:30/11:42 do not reflect the exact 10% gain over 6 hours.

Common Pitfalls:
Adding 3 minutes once instead of per every 30-minute block; mixing shown vs real intervals.

Final Answer:
11:36 am