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(C) Let the ratio in which the two alloys are mixed be $x:y$.In the first alloy,the fraction of zinc is $\frac{2}{2+1} = \frac{2}{3}$.In the second al

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$3:5$

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(C) Let the ratio in which the two alloys are mixed be $x:y$.In the first alloy,the fraction of zinc is $\frac{2}{2+1} = \frac{2}{3}$.In the second alloy,the fraction of zinc is $\frac{4}{4+1} = \frac{4}{5}$.In the final alloy,the fraction of zinc is $\frac{3}{3+1} = \frac{3}{4}$.Using the rule of alligation:Difference between the second alloy and the final alloy: $\frac{4}{5} - \frac{3}{4} = \frac{16-15}{20} = \frac{1}{20}$.Difference between the final alloy and the first alloy: $\frac{3}{4} - \frac{2}{3} = \frac{9-8}{12} = \frac{1}{12}$.The ratio $x:y$ is the ratio of these differences:$x:y = \frac{1}{20} : \frac{1}{12} = 12 : 20 = 3 : 5$.Thus,the alloys should be mixed in the ratio $3:5$.

Two alloys contain zinc and copper in the ratio of $2:1$ and $4:1$. In what ratio should the two alloys be mixed to get a new alloy having zinc and copper in the ratio of $3:1$?

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