Silver and copper alloy mixture

CAT 2021 Slot 3 · QA · Medium · Ratios and proportions

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If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is

  1. A.

    3

  2. B.

    2.5

  3. C.

    4

  4. D.

    3.5

Answer

A

Explanation

Let the weight of the initial alloy be xx kg and its silver percentage be ss.

In the first case, adding 3 kg of pure silver (100% silver): sx+3x+3=0.9  ⟹  sx+3=0.9x+2.7  ⟹  x(0.9−s)=0.3\frac{sx + 3}{x + 3} = 0.9 \implies sx + 3 = 0.9x + 2.7 \implies x(0.9 - s) = 0.3 --(1)

In the second case, adding 2 kg of 90% silver alloy: sx+0.9×2x+2=0.84  ⟹  sx+1.8=0.84x+1.68  ⟹  x(0.84−s)=−0.12  ⟹  x(s−0.84)=0.12\frac{sx + 0.9 \times 2}{x + 2} = 0.84 \implies sx + 1.8 = 0.84x + 1.68 \implies x(0.84 - s) = -0.12 \implies x(s - 0.84) = 0.12 --(2)

Subtracting equation (2) from equation (1): x(0.9−s−(0.84−s))=0.3−0.12x(0.9 - s - (0.84 - s)) = 0.3 - 0.12 x(0.06)=0.18  ⟹  x=3x(0.06) = 0.18 \implies x = 3

Thus, the weight of the initial alloy is 3 kg.

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