We are given two alloys, X and Y, with different proportions of copper (Cu) and zinc (Zn).
- Alloy X contains Cu and Zn in the ratio 5:4.
- Alloy Y contains Cu and Zn in the ratio 5:13.
When equal quantities of alloys X and Y are melted together, we need to find the ratio of Cu to Zn in the resultant alloy Z.
Step-by-Step Solution:
Let the common quantity of each alloy be 1 unit.
In alloy X, the ratio of Cu to Zn is 5:4. Therefore, in 1 unit of X, the quantities are:
- Cu in X = \(\frac{5}{5+4} = \frac{5}{9}\)
- Zn in X = \(\frac{4}{5+4} = \frac{4}{9}\)
In alloy Y, the ratio of Cu to Zn is 5:13. Therefore, in 1 unit of Y, the quantities are:
- Cu in Y = \(\frac{5}{5+13} = \frac{5}{18}\)
- Zn in Y = \(\frac{13}{5+13} = \frac{13}{18}\)
Combine both alloys to find the total Cu and Zn in the new alloy Z:
- Total Cu in Z = \(\frac{5}{9} + \frac{5}{18} = \frac{10}{18} + \frac{5}{18} = \frac{15}{18} = \frac{5}{6}\)
- Total Zn in Z = \(\frac{4}{9} + \frac{13}{18} = \frac{8}{18} + \frac{13}{18} = \frac{21}{18} = \frac{7}{6}\)
The ratio of Cu to Zn in Z is:
- Cu to Zn = \(\frac{5}{6} : \frac{7}{6}\)
- Simplifying, we find Cu:Zn = 5:7.
Therefore, the ratio of Cu to Zn in the new alloy Z is 5:7. Thus, the correct answer is 5:7.
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