A container is full of milk. One third of the milk is taken out and then an equal amount of water is poured into the container to fill it. This operations is repeated for five times. The final ratio of milk and water in the container is :

$\frac{32}{211}$

The correct answer is Option (2) → $\frac{32}{211}$

The successive dilution formula,

$\text{Remaining quantity = Initial quantity} × \left(1-\frac{\text{Removed}}{\text{Total}}\right)^n$

$∴\text{Milk left}=1×(\frac{2}{3})^5=\frac{32}{243}$

Water fraction = $1-\frac{32}{243}=\frac{211}{243}$

$\frac{Milk}{Water}=\frac{211}{243}$