According to law of floation an object floats if its density is less than the density of the liquid or the object has to be specially designed so that it can displace as much liquid to its weight.
egg has density in between density of water and salty water. Water at 4'C has density of 1000 kg/m3 and salty water around 1033kg/m3. When you add salt in the water its density increases and then egg starts to float. When you put lot of salt in the water the egg can completely float.
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