Which two numbers (not the digits of the numbers), from amongst the given options, should be interchanged to make the given equation correct?
13−36+18×24÷6=97

Let's test the options to find which interchange balances the equation correctly using BODMAS rule:
Test Option D (Interchanging 18 and 36):
The equation becomes:

13−18+36×24÷6=97
Applying BODMAS:

Division: 24÷6=4

Equation now: 13−18+36×4

Multiplication: 36×4=144

Equation now: 13−18+144

Addition/Subtraction: 144+13−18=157−18=139
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=97

Let's test Option C (Interchanging 36 and 24):
The equation becomes:

13−24+18×36÷6=97
Applying BODMAS:

Division: 36÷6=6

Equation now: 13−24+18×6

Multiplication: 18×6=108

Equation now: 13−24+108

Addition/Subtraction: 108+13−24=121−24=97

Since 97=97, Option C is correct.