Let's break down the problem step by step to find out the quantity of pure milk added to the vessel.

Step 1: Initial quantities of milk and water

• Initially, the vessel contains 40 liters of pure milk.
• 10 liters of water is added to the vessel, making the total mixture 50 liters, with 40 liters of milk and 10 liters of water.

So, the ratio of milk to water in the vessel is: $\text{Milk:Water} = \frac{40}{10} = 4:1$

Step 2: 25 liters of the mixture is sold

Since the ratio of milk to water is 4:1, out of the 25 liters sold:

• Milk sold = $\frac{4}{5} \times 25 = 20$ liters
• Water sold = $\frac{1}{5} \times 25 = 5$ liters

Step 3: Remaining quantities of milk and water after selling

After selling 25 liters of the mixture, the remaining quantities in the