From a 54-litre container of pure milk, 9 litres are removed and replaced by water . This process is repeated three times in total. What is the final quantity of milk left in the container?

The correct option is 31.25 litres.

Understanding the Formula:
When a container initially holds $V$ litres of pure liquid, and $x$ litres are drawn out and replaced by water $n$ times, the quantity of pure liquid remaining in the container is given by the formula:
$\text{Final Quantity}=V\times {\left(1-\frac{x}{V}\right)}^n$

Given Data:
Initial volume of milk ($V$) = 54 litres
Volume of liquid removed and replaced each time ($x$) = 9 litres
Number of operations ($n$) = 3

Step-by-Step Calculation:

1. Substitute the given values into the formula:
$\text{Remaining Milk}=54\times {\left(1-\frac{9}{54}\right)}^3$

2. Simplify the fraction inside the bracket:
$\frac{9}{54}=\frac{1}{6}$

3. Subtract the fraction from 1:
$1-\frac{1}{6}=\frac{5}{6}$

4. Evaluate the power of 3:
${\left(\frac{5}{6}\right)}^3=\frac{125}{216}$

5. Calculate the final quantity of milk:
$\text{Remaining Milk}=54\times \frac{125}{216}$

Since $\frac{54}{216}=\frac{1}{4}$:
$\text{Remaining Milk}=\frac{125}{4}=31.25\text{litres}$

Therefore, the final quantity of milk left in the container is 31.25 litres.