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

Initial solution content: 30% acid, 70% water.
Volume of acid: \(200 \times 0.3 = 60\) litres.
Volume of water: \(200 \times 0.7 = 140\) litres.

Step 1: Evaporate 20% of water
Evaporated water: \(140 \times 0.2 = 28\) litres.
Remaining water: \(140 - 28 = 112\) litres.
Total volume now: \(60 + 112 = 172\) litres.

Step 2: Extract 10% of acid
Acid extracted: \(60 \times 0.1 = 6\) litres.
Remaining acid: \(60 - 6 = 54\) litres.
Total volume now: \(172 - 6 = 166\) litres.

Step 3: Remove 15% of the solution and replace with water
Solution removed: \(166 \times 0.15 = 24.9\) litres.
Acid in removed solution: \(\frac{54}{166} \times 24.9 \approx 8.1\) litres.
Remaining acid: \(54 - 8.1 = 45.9\) litres.
The removed solution is replaced with 24.9 litres of water.

Final Volume of Acid
Volume of acid in final solution: 45.9 litres.

Verification
The calculated volume of acid, 45.9 litres, falls within the expected range of 45.9,45.9.

Answer 2

Step 1: Understanding the Question:
The problem involves a sequence of operations on a solution of acid and water. We need to track the volume of acid and water through each step to find the final volume of acid. We will calculate the changes step-by-step.
Step 2: Detailed Explanation:
We will break down the problem into the initial state and the three subsequent processes.
Initial State:
Total volume of the solution = 200 litres.
Acid concentration = 30%.
Water concentration = 100% - 30% = 70%.
Initial volume of acid = \(0.30 \times 200\) litres = 60 litres.
Initial volume of water = \(0.70 \times 200\) litres = 140 litres.
Process 1: Evaporation of Water
20% of the water content is evaporated. Only the water volume changes.
Volume of water evaporated = \(0.20 \times 140\) litres = 28 litres.
Remaining volume of water = \(140 - 28\) = 112 litres.
Volume of acid remains the same = 60 litres.
Total volume of the solution after evaporation = \(60 + 112\) = 172 litres.
Process 2: Extraction of Acid
10% of the acid content is removed. Only the acid volume changes.
Volume of acid extracted = \(0.10 \times 60\) litres = 6 litres.
Remaining volume of acid = \(60 - 6\) = 54 litres.
Volume of water remains the same = 112 litres.
Total volume of the solution after extraction = \(54 + 112\) = 166 litres.
Process 3: Removal and Replacement
15% of the resulting solution (166 litres) is removed. This removal affects both acid and water.
Volume of solution removed = \(0.15 \times 166\) litres = 24.9 litres.
The acid removed is 15% of the current acid volume:
Volume of acid removed = \(0.15 \times 54\) litres = 8.1 litres.
The final volume of acid is the volume after this removal:
Final volume of acid = \(54 - 8.1\) = 45.9 litres.
(Note: This removed volume of 24.9 litres is then replaced with water, which changes the final water volume and total volume, but does not affect the final acid volume).
Step 3: Final Answer:
The volume of acid in the final solution is 45.9 litres.