CAT 2021 Slot 3 QA Q1 Ratio, Mixtures & Averages

Question 1 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

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) 3 Ratio, Mixtures & Averages MCQ

Solution

  1. Let the initial alloy weigh \(w\) kg with \(s\) kg of silver.
  2. With 3 kg silver: \(s + 3 = 0.9(w + 3) \Rightarrow s = 0.9w - 0.3\).
  3. With 2 kg of 90% alloy: \(s + 1.8 = 0.84(w + 2) \Rightarrow s = 0.84w - 0.12\).
  4. \(0.9w - 0.3 = 0.84w - 0.12 \Rightarrow 0.06w = 0.18 \Rightarrow w = 3\) kg.

Same concept in other years

See every question on Adding a pure component to shift a mixture's concentration.

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