Q9
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
Answer: D
Key idea: Track the litres of acid; the total volume stays 200 L throughout.
- Initially acid \(=30\%\) of 200 \(=60\) L.
- Replace 20% with water: acid \(=60\times0.8=48\) L.
- Replace 10% (20 L) with acid: 4.8 L acid removed, 20 L acid added, so acid \(=48-4.8+20=63.2\) L.
- Replace 15% with water: acid \(=63.2\times0.85=53.72\) L.
- Percentage \(=\frac{53.72}{200}\times100=26.86\%\approx27\%\).
Tip: Replacing a fraction \(f\) with water simply multiplies the acid by \((1-f)\); only the "replace with acid" step needs an addition.
Hence, the answer is (D) 27.