The problem is poorly formulated. The pingpong ball is attached within the cup, while the metal ball is attached outside of the cup. To make the two sides of the balancing scales equivalent, either the metal ball should rest on a stand inside the cup, or the pingpong ball should be suspended by a pulley system coming from outside the cup. In the former case it is obvious the metal side is heavier; in the latter case, nothing changes since both balls are simply displacing the water, all force differences are being taken up by the suspending devices. Thus, the solution to the problem as given shows the pingpong ball cup being ever so slightly heavier.