Can't We Test The Purity Of Substance By Checking The Density?

In general, you cannot tell anything about the purity of a substance from its density alone.

However, there may be cases where contaminants are of uniformly higher or lower density than the pure substance. In those cases, a change in the density would indicate a mixture rather than a pure substance.

A measurement of density, among other measurements, might be something that one would look at to determine purity. A pure substance will have a certain set of properties. If the density of a sample is wrong, the sample is certainly not pure. If the density is right, you need to check other properties, too.