From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of mixture is:

• Let the total quantity of the mixture be x liters.
• After first operation: 6 liters of milk is removed and replaced with water.
• Milk left = (1 - 6/x) of original milk.
• After second operation: again 6 liters of mixture removed and replaced.
• Milk left = (1 - 6/x)2 of original milk.
• Final milk to total mixture ratio is 9 : 16 ⇒ milk = (9/25)x

Now equate:

(1 - 6/x)² = 9/25
√(1 - 6/x)² = √(9/25)
1 - 6/x = 3/5
6/x = 1 - 3/5 = 2/5
x = 15

Answer: 15 liters

The total quantity of the mixture is 15 liters.