Multiple choice

An alloy contains copper, zinc and tin in the ratio 4 : 5 : 6 respectively. Another alloy containing copper and tin is melted and mixed with the first alloy. If the mixture contains copper, zinc and tin in the ratio 13 : 1 : 3, find the ratio of copper and tin in the second alloy.

  1. 12 : 5

  2. 9 : 25

  3. 25 : 9

  4. 61 : 9

  5. None of these
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D Correct answer
Explanation

Let alloy 1 be 4x, 5x, 6x. Total = 15x. Let alloy 2 be C2, T2. Mixture: (4x + C2) / (5x) / (6x + T2) = 13 : 1 : 3. From zinc: 5x / Total_mixture = 1 / 17. Total_mixture = 85x. So, (4x + C2) + 5x + (6x + T2) = 85x. C2 + T2 = 70x. Using copper: (4x + C2) / 5x = 13 / 1 => 4x + C2 = 65x => C2 = 61x. Then T2 = 70x - 61x = 9x. Ratio C2 : T2 = 61 : 9.

AI explanation

Since the final mixture has a zinc ratio of 1 and the first alloy has a zinc ratio of 5, the first alloy must be diluted by a factor of 5 to achieve the final ratio. This means the first alloy is mixed with the second alloy in a 1 to 4 ratio, giving the second alloy a weight of 4 units. The first alloy contributes 4 copper, 1 zinc, and 6 tin, while the final mixture contains 65 copper, 5 zinc, and 15 tin. By subtracting the first alloy's contribution from the final mixture, the second alloy contains 61 copper and 9 tin. The ratio of copper to tin in the second alloy is 61 to 9.

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