Question

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?

• A. \(25\)
• B. \(27\)
• C. \(29\)
• D. \(23\)

Hint:

In replacement problems, always track the \emph{amount} of the substance (here, acid) after each step. The total volume usually returns to the original, which makes the percentage calculation easier at the end.

Answer 1

The Correct Option is B

Approach (work with the acid fraction and multipliers in one chain): Since volume is fixed at 200 L, follow the acid concentration as a fraction; a water-replacement just scales it, an acid-replacement scales then adds.

Step 1: Start at fraction $0.30$ acid.

Step 2: Replace $20\%$ with water $\to$ fraction $\times 0.8 = 0.30 \times 0.8 = 0.24$.

Step 3: Replace $10\%$ with acid. Removing $10\%$ scales acid to $0.24 \times 0.9 = 0.216$; adding $10\%$ pure acid raises the fraction by $0.10$: $0.216 + 0.10 = 0.316$.

Step 4: Replace $15\%$ with water $\to$ fraction $\times 0.85 = 0.316 \times 0.85 = 0.2686$.

Step 5: That is $26.86\%$, nearest to $27\%$.

Answer: About $27\%$ acid in the final solution.