A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

$\frac{16}{65}$

$\text{Each time, }\frac{1}{3}\text{ of milk is replaced by water}.$

$\text{Fraction of milk left after one operation}=\frac{2}{3}.$

$\text{After 4 repetitions, fraction of milk left}=\left(\frac{2}{3}\right)^4.$

$=\frac{16}{81}.$

$\text{Fraction of water} = 1-\frac{16}{81}=\frac{65}{81}.$

$\text{Final ratio of milk : water }=16:65.$

$\text{Final ratio }=16:65.$