Which of the following interchanges of numbers would make the given equation correct?
$$8\times 20÷3+9-5=38$$

Let's test the options using the BODMAS rule to find the correct configuration.
Given expression: $8\times 20÷3+9-5=38$

* Test Option D (Interchanging 3 and 9):
The equation becomes:

$$8\times 20÷9+3-5=38$$

$$\frac{160}{9}+3-5\ne 38$$

* Test Option C (Interchanging 3 and 5):
The equation becomes:

$$8\times 20÷5+9-3=38$$

Applying BODMAS, first division:

$$20÷5=4$$

Next, multiplication:

$$8\times 4=32$$

Next, addition and subtraction:

$$32+9-3=41-3=38$$

Since LHS = RHS = 38, interchanging 3 and 5 makes the mathematical equation correct.