In a mixture 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` ?

Options

A. 72 litres
B. 24 litres
C. 15 litres
D. 1.5 litres

Answer

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

### Step 1: Determine the quantities of milk and water in the initial mixture.
Given the ratio of milk to water is \(4:1\) in a total mixture of \(45\) liters.

- The total parts in the ratio = \(4 + 1 = 5\).
- Each part represents \( \frac{45 \text{ liters}}{5} = 9 \text{ liters}\).

Now, we can find the quantities:
- Milk = \(4 \times 9 = 36 \text{ liters}\)
- Water = \(1 \times 9 = 9 \text{ liters}\)

### Step 2: Set up the equation for the new ratio after adding water.
We want to find out how much water (let's call it \(x\) liters) needs to be added to make the new ratio of milk to water equal to \(3:2\).

After adding \(x\) liters of water, the new quantities will be:
- Milk = \(36 \text{ liters}\) (remains the same)
- Water = \(9 + x \text{ liters}\)

### Step 3: Write the equation based on the new ratio.
According to the new ratio \(3:2\):
\[ \frac{\text{Milk}}{\text{Water}} = \frac{3}{2} \]
Substituting the values we have:
\[ \frac{36}{9 + x} = \frac{3}{2} \]

### Step 4: Cross-multiply to solve for \(x\).
Cross-multiplying gives us:
\[ 36 \times 2 = 3 \times (9 + x) \]
This simplifies to:
\[ 72 = 27 + 3x \]

### Step 5: Isolate \(x\).
Now, we will isolate \(x\):
\[ 72 - 27 = 3x \]
\[ 45 = 3x \]
\[ x = \frac{45}{3} = 15 \]

### Conclusion:
Therefore, the amount of water that must be added to make the mixture ratio \(3:2\) is \(15\) liters.

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