An alloy contains zinc and copper in the ratio 3 : 8 and another alloy contains zinc and copper in the ratio 7 : 15.
- 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.
- 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.
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
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Posted by Charlie
on 2012-12-14 12:42:26 |
solution
