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These problems relate to objects of different weight, and using a balanced scale to determine the odd item, be it a false coin, or an under-filled sack of grain. (Usually it's coins though)

Alloy 1 contains copper and zinc in the ratio N-1:N and Alloy 2 contains copper and zinc in the ratio N:N+1, where N is a positive integer > 1.
(i) Alloy 1 and Alloy 2 are melted together in the ratio P:Q, so that the ratio of copper and zinc in the resulting alloy is P:Q.
(ii) Alloy 1 and Alloy 2 are melted together in the ratio P:Q, so that the ratio of copper and zinc in the resulting alloy is Q:P.
In each of the cases (i) and (ii) - determine p:q in terms of N.
*** Each of p and q is a positive integer.

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