CAT 2025 Slot 1 · Quant · Question 9

CAT 2025 Slot 1 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to
  1. A
    23
  2. B
    25
  3. C
    29
  4. D
    27
Pick an option, then check.
Answer & solution

Answer: Option D

The volume stays 200 litres throughout, so just track the litres of acid. Start with 0.3\times 200=60 litres of acid.

Step 1. Remove 20\% of the solution, that is 40 litres, which carries away 20\% of the acid: 60\times 0.8=48 litres of acid left. Water is added back, so acid stays 48.

Step 2. Remove 10\% of the solution, taking 10\% of the acid: 48\times 0.9=43.2. Now 20 litres of pure acid go in: 43.2+20=63.2 litres.

Step 3. Remove 15\%, taking 15\% of the acid: 63.2\times 0.85=53.72 litres. Water is added back, so acid stays 53.72.

The final strength is \frac{53.72}{200}=26.86\%, nearest to 27.

Only step 2 adds acid; the other two simply scale it down.

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