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

The correct answer is 27.

Let's break down the process step-by-step to track the amount of acid in the container after each replacement.

Initially, the container holds 200 litres of solution with 30% acid.

Initial amount of acid:

$30\%\text{ of }200=\frac{30}{100}\times 200=60\text{ litres}$

Step 1: Replace 20% of the solution with water
When 20% of the solution is removed, 20% of the acid inside it is also removed. This means 80% of the acid remains.

Amount of acid remaining after the removal:

$60\times 0.80=48\text{ litres}$

The total volume is restored to 200 litres by adding water, so there are 48 litres of acid in the 200 litres of solution.

Step 2: Replace 10% of the resulting solution with acid
Removing 10% of the new solution removes 10% of the current acid, leaving 90% of the acid behind.

Amount of acid remaining before adding new acid:

$48\times 0.90=43.2\text{ litres}$

The removed 10% of the total solution is equivalent to 20 litres. Since this 20 litres is replaced entirely with pure acid, we must add it to the remaining acid.

Amount of acid after Step 2:

$43.2+20=63.2\text{ litres}$

Step 3: Replace 15% of the solution with water
Removing 15% of the solution removes 15% of the acid, leaving 85% of it behind.

Amount of acid after Step 3:

$63.2\times 0.85=53.72\text{ litres}$

The total volume is again restored to 200 litres with water.

Final Calculation:
Now, we find the final percentage of acid by volume in the 200-litre container.

$\text{Percentage}=\left(\frac{53.72}{200}\right)\times 100\%=26.86\%$

The nearest integer to 26.86% is 27%.