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 Ratio Resolution III (Posted on 2012-12-14)
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.

 See The Solution Submitted by K Sengupta No Rating

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 solution | Comment 1 of 2

First alloy: 3/11 zinc, 8/11 copper
Second alloy: 7/22 zinc, 15/22 copper

`mixture                                                scenario                                                   1              2p/(p+q) * 3/11 + q/(p+q) * 7/22 zinc           = p/(p+q)      = q/(p+q)`
`p/(p+q) * 8/11 + q/(p+q) * 15/22 copper        = q/(p+q)      = p/(p+q)`
`1. 3p/11 + 7q/22 = p       so  7q/22 = 8p/11   8p/11 + 15q/22 = q      so  8p/11 = 7q/22`

p/q = (7*11)/(22*8) = 7/16 or 7:16

`   2. 3p/11 + 7q/22 = q       so  3p/11 = 15q/22`
` `

p/q = (15*11)/(22*3) = 15/6 or 15:6

 Posted by Charlie on 2012-12-14 12:42:26

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