Question

A 200-litre container holds a solution that is 30% acid and the rest water. The solution undergoes the following three processes sequentially:
1. 20% of the water content is evaporated.
2. From the remaining mixture, 10% of the acid content is chemically extracted and removed.
3. Finally, 15% of the resulting solution is removed and replaced with water.
What is the volume of acid in the final solution?

Hint:

In multi-step mixture problems, always keep a clear record of the volume of each component (e.g., acid, water) and the total volume after each step. Pay close attention to what each percentage refers to—the total solution, a specific component, etc.

Answer 1

Correct Answer: 45.9

Step 1: Start: \(200\) L total, acid \(=30\% \times 200=60\) L, water \(=140\) L. Evaporate \(20\%\) of the water: water lost \(=0.2 \times 140=28\) L, so water \(=112\) L, acid stays \(60\) L (total \(=172\) L).
Step 2: Extract \(10\%\) of the acid: acid lost \(=0.1 \times 60=6\) L, so acid \(=54\) L (total \(=166\) L, water still \(112\) L).
Step 3: Remove \(15\%\) of this \(166\) L solution and top up with water. Acid removed \(= 0.15 \times 54=8.1\) L, leaving acid \(=54-8.1=45.9\) L (total volume stays \(166\) L once water is topped up).
Final Answer: \[ \boxed{45.9 \text{ litres of acid}} \]