Milk and water are in 7:2 ratio in a mixture of 729 litres. How much water shall be mixed in it in order to change this ratio to 7:3?

Let's break down the problem step by step.

### Step 1: Understanding the current composition
The current mixture contains milk and water in the ratio of 7:2, and the total volume is 729 litres.

- Let the amount of milk be \( 7x \) and the amount of water be \( 2x \), where \( x \) is a common factor.
- We know that:
  \[
  7x + 2x = 729
  \]
  \[
  9x = 729
  \]
  \[
  x = \frac{729}{9} = 81
  \]

- Therefore, the current amount of milk is:
  \[
  7x = 7 \times 81 = 567 \text{ litres}
  \]
- The current amount of water is:
  \[
  2x = 2 \times 81 = 162 \text{ litres}
  \]

### Step 2: New ratio of 7:3
We want to change the ratio of milk to water to 7:3. The amount of milk will remain the same, but we need to add more water.

Let the new amount of water be \( W \). So, according to the new ratio:

\[
\frac{567}{W} = \frac{7}{3}
\]

Cross-multiply to solve for \( W \):

\[
567 \times 3 = 7 \times W
\]
\[
1701 = 7W
\]
\[
W = \frac{1701}{7} = 243 \text{ litres}
\]

### Step 3: Amount of water to be added
The current amount of water is 162 litres, and we need a total of 243 litres. So, the additional water required is:

\[
243 - 162 = 81 \text{ litres}
\]

### Final Answer:
To change the ratio to 7:3, you need to add **81 litres** of water.

---

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions for deeper exploration:
1. What would happen if you increased the amount of water by more than 81 litres?
2. How would the solution change if the original ratio was 5:2 instead of 7:2?
3. Can you determine the amount of water needed if the total volume was different?
4. How does the new water amount affect the overall density of the mixture?
5. What is the new total volume of the mixture after adding the water?

**Tip:** Ratios can be scaled up or down proportionally, so always check total quantities when ratios change.

Find out how much water is needed to change the milk and water ratio from 7:2 to 7:3 in a 729-litre mixture. This problem involves ratio and proportion concepts, with a detailed solution. Ideal for students in Grades 6-8.

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