To find the time it takes for the man to cover the same distance running at 16.5 km/h, follow these steps:

1. Calculate the Distance:
- The man's walking speed is 4 km/h, and he covers the distance in 2 hours and 45 minutes.
- Convert 2 hours and 45 minutes to hours:
\[
2 \text{ hours} + \frac{45}{60} \text{ hours} = 2 + 0.75 = 2.75 \text{ hours}
\]
- Use the formula for distance: \( \text{Distance} = \text{Speed} \times \text{Time} \)
\[
\text{Distance} = 4 \text{ km/h} \times 2.75 \text{ hours} = 11 \text{ km}
\]

2. Calculate the Time to Cover the Same Distance Running:
- The running speed is 16.5 km/h.
- Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)
\[
\text{Time} = \frac{11 \text{ km}}{16.5 \text{ km/h}} = \frac{11}{16.5} \text{ hours}
\]
- Simplify \( \frac{11}{16.5} \):
\[
\frac{11}{16.5} = \frac{11}{\frac{33}{2}} = \frac{11 \times 2}{33} = \frac{22}{33} = \frac{2}{3} \text{ hours}
\]
- Convert \( \frac{2}{3} \text{ hours} \) to minutes:
\[
\frac{2}{3} \text{ hours} \times 60 \text{ minutes/hour} = 40 \text{ minutes}
\]


The man will cover the same distance in 40 minutes when running at 16.5 km/h.

The correct answer is A. 40 min.