To determine C's share of the profit, follow these steps:

1. Calculate the Total Investment:
- A's investment: N36,000
- B's investment: N45,000
- C's investment: N54,000

Total investment = N36,000 + N45,000 + N54,000 = N135,000

2. Determine the Ratio of Each Partner's Investment:
- A's share ratio = \( \frac{36,000}{135,000} \)
- B's share ratio = \( \frac{45,000}{135,000} \)
- C's share ratio = \( \frac{54,000}{135,000} \)

Simplify these ratios:
- A's share ratio = \( \frac{36,000}{135,000} = \frac{4}{15} \)
- B's share ratio = \( \frac{45,000}{135,000} = \frac{1}{3} = \frac{5}{15} \)
- C's share ratio = \( \frac{54,000}{135,000} = \frac{6}{15} \)

3. Calculate C's Share of the Profit:
- Total profit = N37,500
- C's share = \( \frac{6}{15} \times 37,500 \)

Perform the multiplication:
\[
C's \, share = \frac{6}{15} \times 37,500 = \frac{6 \times 37,500}{15} = \frac{225,000}{15} = 15,000
\]


C's share of the profit is N15,000.

The correct answer is B. N15,000.