A vessel of 160 L is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found out that the vessel is vacated by 55%, then the quantity of milk and water in the original mixture is

The total volume of the mixture is 160 L and 70% of the milk and 30% of the water is removed. With this, 55% of the vessel is vacated, so 45% of the original mixture remains, which is 72 L.

Let the amount of Milk in the original mixture be $$x$$ liters so the amount of water in the vessel would be $$160-x$$ liters. 

Milk removed = 70% of $$x$$ = $$0.7x$$

Water removed = 30% of $$160-x$$ = 0.3(160−x).

Remaining milk: x − 0.7x = 0.3x

Remaining water: 160 − x − 0.3(160−x) = 0.7(160−x)

The remaining mixture is 72 liters. 

0.3x + 0.7(160−x) = 72

Upon solving, we get, x = 100

Therefore, the amount of Milk is 100 liters and the amount of water = 160 - 100 = 60 liters.