

For an object to float on a liquid, the liquid must be more dense than the whole of the object and the air contained within it. In normal water, its particles are spread out so it's not that dense. This means, at first the water is less dense than the eggs, which is why they sink. But with each spoonful of salt you add, the water increases in density. When enough salt has been added, the salt water will eventually become more dense than the object, and so it can now float.
This experiment should be done OUTSIDE - as things could get messy!
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