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