Is it possible to calculate the weight of the metal & non metal in
the weighing balance?
To discern the separate weights of two elements, emulate Archimedes.
You will need a scale and an apparatus to measure displacement of
volume. First, weigh the piece. Then measure the volume displacement
of the piece. Knowing the volume displacement of the constituent
metal per gram you can calculate what the displaced volume ought to
be if the piece were made only of that metal. Subtract the calculated
displacement from the measured displacement. The result is the
displacement of the stones. By using the known displacement of those
stones per gram you can arrive at the weight of the stones.