An alloy contains zinc and copper in the ratio 3 : 8 and another alloy contains zinc and copper in the ratio 7 : 15.

1. When the two alloys are melted together in the ratio p:q, then the ratio of zinc and copper in the resulting alloy is p:q. Determine, with proof, the ratio p:q.
2. What is the ratio p:q, if keeping all the other conditions in (i) unaltered, the ratio of zinc and copper in the resulting alloy is q:p?

Note: Assume that p and q does not have any common factor > 1.