There are 81 litre pure milk in a container. One ­third of milk is replaced by water in the container. Again one­third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture ?

using $$\frac{QNR final}{Total} = \frac{QNR initial}{Total}(1- \frac{quantity replaced}{total})^n$$

here QNR is the quantity which is only removed in whole process and hence here it is milk and 'n' is the number of times the replacement process is repeated

So using the formula

$$\frac{QNR final}{Total}$$ = $$\frac{81}{81}$$ x $$(1- \frac{27}{81})^2$$

$$\frac{QNR final}{Total}$$ = 4/9

So after two replacement cycles the ratio of Milk : Water = 4:5