Swimming in the Dead Sea

Water particles are much bigger than the atoms salt consists of (sodium and chlorine). Due to this fact the atoms of sodium and chlorine disperse between the water particles (similar to the sugar particles between the peas). The volume of the liquid substance has barely changed by the addition of salt but its density has increased.

Therefore the density of seawater is greater than the density of tap water.
The grape is swimming on the water surface just because of the same reason as the newspaper reading man in the Dead Sea does: The density of salt water is greater than the density of the swimming body!