Why does the egg sink in tap water but floats in salt water?

The egg has density which is denser than tap water and is more compact in terms of g/cm3. But after salt is added to tap water and mixed, the less dense salt makes the combined density of the tap water and salt lesser than the egg although the mass of the salt water has increased from that of the tap water. As objects which are less dense floats on denser objects, the egg floats on the salt water.

Why and how does the density of the water change when salt was added to the water?

Salt has and density which lesser than water thus making it less dense. As Density=Mass/Volume, g/cm 3 of salt lesser than water. Therefore, when salt is added to water, is stirred and mixed, their combined Mass/Volume or rather density per g/cm3 is lesser than the oure water before .