X mass of water is added to the fluid volume, but at the cost of more than the volume of X of water - the ice is less dense than water, remember?
Dude, did you not hear what I said.
Look up Archimedes' Principle. How many times do I have to explain it?
A buoyant object displaces its weight in water. If the object weighs 100g, then 100mL of water (assuming 1g/mL is the density of water) is displaced by it. If the object sheds 100g (100mL) of water, then the object also displaces 100g (100mL) less water. It balances out. It does not matter if the object is slightly more dense than pure ice is, as long as it is floating.
You have, say, 1000mL of water. You have an object weighing 100g. This object will -- assuming it is buoyant, which in this case it is -- displace 100g (100mL) of water. The total volume of the water and the part of the object that is submerged is the total of the surrounding water (1000mL) and the volume displaced below the surface by the object (100mL), or 1100mL.
10g of the object melts into water equivalent to the water it is floating in. This adds 10mL of water to the surrounding water. However, the object now only weighs 90g. There is now less of the object underwater, as only 90g (90mL) of water is being displaced by it. The total volume of the water and the part of the object that is submerged is the total of the surrounding water (1110mL) and the volume displaced below the surface by the object (90mL), or 1100mL.
The fact that there is a stone buried in the ice is 100% irrelevant to what I am saying here, unless it causes the density of the object as a whole to go below that of water, which is not the case.
This really isn't even contestable. This is all just a basic Archimedes' Law question at this point, with the original question being a sort of logic/scientific understanding puzzle.