An alloy contains copper and zinc in the ratio of 4:3 and another contains copper and tin in the ratio of 9:5. If equal weights of the two are melted together to form a new alloy, find the weight of tin per kg in the new alloy.
Solution
Correct Answer: Option D
∵ Equal weights of two alloys are melted together to form a new alloy, let the weights of both the alloys taken be x kg
In the x kg of first alloy, weight of copper \(= \frac{4}{{4 + 3}} \times x = \frac{{4x}}{7}\) kg
Weight of zinc in x kg of first alloy \(= x - \frac{{4x}}{7} = \frac{{3x}}{7}\) kg
Similarly, in x kg of second alloy, weight of copper \(= \frac{9}{{9 + 5}} \times x = \frac{{9x}}{{14}}\) kg
Weight of tin in x kg of second alloy \(= x - \frac{{9x}}{{14}} = \frac{{5x}}{{14}}\) kg
When the two alloys are melted and fused together, the amount of tin in the total mixture will not change.
Total weight of the mixture = x + x = 2x kg
∴ratio of weight of tin to total weight \(= \frac{{\frac{{5x}}{{14}}}}{{2x}} = \frac{5}{{28}}\)
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