To find the final volume of chemical $B$, we can first calculate the remaining volume of chemical $A$ after the replacement process is completed.

Step 1: Understand the given parameters

• Initial volume of chemical $A$ ($V$) = $10$ litres.
• Total volume of the mixture in the container remains constant at $10$ litres.
• Volume replaced in each step ($x$) = $1$ litre.
• Number of times the process is performed ($n$) = $3$ (The first replacement, then a second replacement, and then performed "once more").

Step 2: Apply the replacement formula The formula for the amount of the original liquid remaining after $n$ replacements is given by: $\text{Final Amount of } A = \text{Initial Amount} \times \left(1 - \frac{x}{V}\right)^n$

Substitute the values into the formula: $A_3 = 10 \times \left(1 - \frac{1}{10}\right)^3$ $A_3 = 10 \times \left(\frac{9}{10}\right)^3$ $A_3 = 10 \times \frac{729}{1000}$ $A_3 = 7.29 \text{ litres}$

Step 3: Calculate the volume and percentage of chemical $B$ Since the total volume of the mixture is always $10$ litres, the volume of chemical $B$ present in the container after $3$ operations is: $\text{Volume of } B = \text{Total Volume} - \text{Final Amount of } A$ $\text{Volume of } B = 10 - 7.29 = 2.71 \text{ litres}$

Now, convert this volume into a percentage of the total mixture: $\text{Percentage of } B = \left(\frac{2.71}{10}\right) \times 100 = 27.1\%$

Approximately, the percentage of chemical $B$ is $27\%$.

Therefore, the correct option is B.