Question

If objects of the same volume displace the same amount of water,the how did Archimedes's gold crown experiment work?

Answer 1

Archimedes gold crown experiment was to check whether the crown was with pure gold or not.
If the crown was pure it will displace a specific volume of water which is equal to the mass x density of pure gold. If the crown had impurities, it will displace a different volume of water which is equal to
(mass of impurity x density of impurity) + (mass of pure gold x density of pure gold).

In the experiment Archimedes didn't get the expected value which meant the crown was impure.