In a maximum of 45 litres, the ratio of milk and water is 4 : 1 How much water must be added to make the mixture ratio 3: 2?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the initial ratio of milk and water
The initial ratio of milk to water is given as 4:1. This means for every 4 parts of milk, there is 1 part of water.

### Step 2: Calculate the total parts in the ratio
The total parts in the ratio of milk and water is:
\[ 4 + 1 = 5 \]

### Step 3: Determine the amount of milk and water in 45 liters
To find the amount of milk and water in 45 liters, we can use the ratio:
- Amount of milk:
\[ \text{Milk} = \frac{4}{5} \times 45 = 36 \text{ liters} \]
- Amount of water:
\[ \text{Water} = \frac{1}{5} \times 45 = 9 \text{ liters} \]

### Step 4: Set up the new ratio after adding water
We want to change the ratio of milk to water to 3:2. The amount of milk remains the same (36 liters), and we will denote the amount of water after adding some water as \( 9 + x \), where \( x \) is the amount of water we need to add.

### Step 5: Write the equation based on the new ratio
The new ratio of milk to water can be expressed as:
\[ \frac{36}{9 + x} = \frac{3}{2} \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 36 \cdot 2 = 3 \cdot (9 + x) \]
This simplifies to:
\[ 72 = 27 + 3x \]

### Step 7: Solve for \( x \)
Subtract 27 from both sides:
\[ 72 - 27 = 3x \]
\[ 45 = 3x \]
Now, divide by 3:
\[ x = \frac{45}{3} = 15 \]

### Step 8: Conclusion
Therefore, the amount of water that must be added to make the mixture ratio 3:2 is **15 liters**.

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