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Ratio Resolution III (Posted on 2012-12-14) Difficulty: 3 of 5
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    
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Solution solution | Comment 1 of 2

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

mixture                                                scenario
                                                   1              2
p/(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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