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
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Official Correct Answer: A. The problem says there's a container with 200 liters of a solution that's 30% acid. So, first, We find out how much acid and water are in the initial solution.
30% of 200 liters is acid. So, 0.3 * 200 = 60 liters of acid. That means the rest is water, which is 200 - 60 = 140 liters of water.
Now, Atul is going to make three replacements. Let me break each step down.
**First Replacement: Replaces 20% of the solution with water.**
20% of 200 liters is 0.2 * 200 = 40 liters. So, he's removing 40 liters of the solution and replacing it with water.
But wait, the solution is 30% acid, so when he removes 40 liters, he's removing 30% acid and 70% water.
So, acid removed: 0.3 * 40 = 12 liters. Water removed: 0.7 * 40 = 28 liters.
After this replacement, the remaining acid is 60 - 12 = 48 liters. The water becomes 140 - 28 + 40 (since he added 40 liters of water) = 140 - 28 = 112 + 40 = 152 liters.
So, after the first replacement, the solution is 48 liters acid and 152 liters water, totaling 200 liters again.
**Second Replacement: Replaces 10% of the resulting solution with acid.**
10% of 200 liters is 20 liters. So, he's adding 20 liters of pure acid.
So, acid becomes 48 + 20 = 68 liters. Water remains 152 liters.
Now, the solution is 68 liters acid and 152 liters water.
**Third Replacement: Replaces 15% of the solution with water.**
15% of 200 liters is 30 liters. So, he's removing 30 liters of the current solution and replacing it with water.
The current solution is 68% acid and 32% water. So, in the 30 liters removed:
Acid removed: 0.68 * 30 = 20.4 liters. Water removed: 0.32 * 30 = 9.6 liters.
So, after this replacement, acid becomes 68 - 20.4 = 47.6 liters. Water becomes 152 - 9.6 + 30 = 152 - 9.6 = 142.4 + 30 = 172.4 liters.
Now, the total acid is 47.6 liters in 200 liters solution. To find the percentage:
(47.6 / 200) * 100 = 23.8%.
Looking at the options, 23.8 is closest to 24%, but the options are A)27, B)25, C)29, D)23. So, 23.8 is nearest to 24, but since 24 isn't an option, the closest is D)23.
Wait, but the correct answer is supposed to be A)27. Did I make a mistake somewhere?
First replacement: 20% removed, which is 40 liters. Acid removed: 12 liters, so 60-12=48. Water: 140-28+40=152. That seems right.
Second replacement: 10% added, 20 liters acid. So, 48+20=68 acid, 152 water. Correct.
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