In the initial mixture, the ratio of milk to water is 7:2. This means that there are 7 parts of milk and 2 parts of water in the mixture.

Given that the total volume of the mixture is 729 liters, we can calculate the amount of milk and water in the initial mixture as follows:

Amount of milk = (7/9) * 729 = 7 * 81 = 567 liters Amount of water = (2/9) * 729 = 2 * 81 = 162 liters

Now, we want to add some water to this mixture to achieve a new ratio of milk to water, which is 7:3.

Let's denote the amount of water to be added as "x" liters. Since we want the ratio of milk to water to be 7:3 in the new mixture, the amount of milk in the new mixture remains the same (567 liters), and the amount of water should be (3/7) times the amount of milk. So, we have:

Amount of water in the new mixture = (3/7) * Amount of milk in the new mixture

Now, let's calculate the amount of milk in the new mixture:

Amount of milk in the new mixture = 567 liters (unchanged)

Amount of water in the new mixture = (3/7) * 567 = 243 liters

In the new mixture, there are already 162 liters of water from the initial mixture. To achieve the desired ratio, we need to add 243 - 162 = 81 liters of water.

So, you need to add 81 liters of water to the initial mixture to get a new mixture containing milk and water in the ratio 7:3