Explain how mixture melting points can be used to distinguish between two compounds

generally melting point of mixture is always different from melting point of pure compound

lets say you have a two compounds called A and B

and you have a unknown compound called X which can be either A or B

now your target is to find unknown is really A or B right?

take some amount of X and mix it with A and B separately

out of these two mixtures one will be pure compound (because we initially assume that unknown can be either A or B)

suppose X + A is same melting with A then X is A

X +B will be less than the melting point of A or

suppose X+B is same melting point like B then X is B

X+A will be less than melting point of B