CAT 2024 Slot 2 QA Q19 Ratio, Mixtures & Averages

Question 19 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
  1. A
    5 : 3
  2. B
    4 : 5
  3. C
    5 : 4
  4. D
    3 : 5

Answer: (D) 3 : 5 Ratio, Mixtures & Averages MCQ

Solution

  1. Let the original solution have acid \(a\) and water \(w\) litres.
  2. After adding 2 L water, 50% acid: \(a = w + 2\).
  3. After adding 15 L acid, 80% acid means acid = 4 times water: \(a + 15 = 4(w+2)\).
  4. Substitute: \(w + 17 = 4w + 8 \Rightarrow w = 3\), \(a = 5\). Water : acid \(= 3:5\).

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