A and B are two metallic pieces. They are fully immersed in water and then weighed. Now they show same loss of weight. The conclusion therefore is:
A and B have equal volumes
Loss of weight is always equal to the upward buoyant force provided by the water which is equal to the weight of water displaced.
Given the loss of weight is equal we know that both of the pieces displaced the same weight of water or the same volume of water.
This implies that their volumes should be equal.