(i) By the problem:
The ratio of zinc and copper in the resulting alloy is
3p/11 + 7q/22
-------------
8p/11 + 15q/22
Accordingly by the given conditions, we must have:
3p/11 + 7q/22 p
------------- = --- ----(A)
8p/11 + 15q/22 q
Applying componendo to both sides of (A), we have:
p + q p + q
------------- = -------
8p/11 + 15q/22 q
Now p+q = 0 forces p = -q, which is a contradiction.
Consequently, 8p/11 + 15q/22 = q, giving:
8p/11 = 7q/22, so that:
p/q = (7*11)/(22*8) = 7/16
Therefore, the required ratio is 7:16
(ii) By the problem:
3p/11 + 7q/22 q
--------------- = ---- ----- (B)
8p/11 + 15q/22 p
Applying componendo to both sides of (B), we have:
p + q p + q
-------------- = -------
8p/11 + 15q/22 p
Now p+q =0 forces p= -q, which is a contradiction.
Consequently, 8p/11 + 15q/22 = p, giving:
15q/22 = 3p/11, so that:
p/q = (15*11)/(22*3) = 5/2
Therefore, the required ratio is 5:2
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