A vessel contains 60 litres of milk. 6 litres of milk is taken out and 6 litres of water is added to the vessel. Again 6 litres of mixture from the vessel is withdrawn and 6 litres of water is added to the vessel. The ratio of milk and water in the resulting mixture in the vessel is

If we are taking out 6 litres out of a 60 litre solution and replacing it with water,

=> We are replacing $$\frac{1}{10}$$th of the solution with water

=> Fraction of milk will become $$\frac{9}{10}$$th of original.

If the process is repeated 'n' times, fraction of milk will become $$(\frac{9}{10})^n$$ of the original.

Here, the process is done twice.

=> Final quantity of milk = $$(\frac{9}{10})^2 \times 60$$ = 48.6 litres

and Final quantity of water = 60 - 48.6 = 11.4 litres

$$\therefore$$ Required ratio = $$\frac{48.6}{11.4}$$ = 81 : 19