Let the two numbers be \( x \) (the smaller number) and \( y \) (the larger number).

We have two pieces of information:
1. The product of the two numbers is 9375:
\[
x \times y = 9375
\]

2. The quotient when the larger number is divided by the smaller is 15:
\[
\frac{y}{x} = 15 \quad \text{or} \quad y = 15x
\]

Substitute \( y = 15x \) into the product equation:
\[
x \times 15x = 9375
\]
\[
15x^2 = 9375
\]
\[
x^2 = \frac{9375}{15} = 625
\]
\[
x = \sqrt{625} = 25
\]

Using \( x = 25 \) to find \( y \):
\[
y = 15x = 15 \times 25 = 375
\]

Now, find the sum of the two numbers:
\[
x + y = 25 + 375 = 400
\]


The sum of the two numbers is 400.

The correct answer is C. 400.