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:
$$\frac{y}{x}=15\text{or}y=15x$$

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.