CAT 2021 Slot 3 · Quant · Question 1

CAT 2021 Slot 3 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
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
Pick an option, then check.
Answer & solution

Answer: Option A

Let the initial alloy weigh w kg and contain s kg of silver.

First mixture: adding 3 kg of pure silver gives \frac{s+3}{w+3}=0.9,

so s+3=0.9w+2.7 and s=0.9w-0.3.

Second mixture: 2 kg of a 90\% alloy carries 1.8 kg of silver,

so \frac{s+1.8}{w+2}=0.84, giving s+1.8=0.84w+1.68.

Substituting the first result into the second: 0.9w-0.3+1.8=0.84w+1.68,

so 0.06w=0.18 and w=3 kg.

Note that we never need the silver percentage of the original alloy, only the amount s.

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