A mixture of milk and water contains `55%` milk and remaining water. How much water should be added (in percentage ) in mixture to reverse the proporation of milk and water ?

Options

A. `25%`
B. `37.5%`
C. `27%`
D. `22%`

Explanation

To solve the problem of how much water should be added to a mixture of milk and water to reverse the proportion of milk and water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Mixture**:
The mixture contains 55% milk and 45% water. This means that in a total of 100 liters of the mixture, there are 55 liters of milk and 45 liters of water.

2. **Determine the Desired Proportion**:
To reverse the proportion of milk and water, we want the new mixture to contain 45% milk and 55% water.

3. **Set Up the Equation**:
Let \( x \) be the amount of water (in liters) to be added to the mixture. After adding \( x \) liters of water, the total volume of the mixture becomes \( 100 + x \) liters.

4. **Calculate the New Proportion of Milk**:
The amount of milk remains the same at 55 liters. The new percentage of milk in the mixture can be expressed as:
\[ \text{Percentage of Milk} = \frac{55}{100 + x} \times 100 \]

5. **Set Up the Equation for the Desired Percentage**:
We want this percentage to equal 45%:
\[ \frac{55}{100 + x} \times 100 = 45 \]

6. **Solve the Equation**:
\[ 55 = 45 \times \frac{100 + x}{100} \]
\[ 55 = 45 + 0.45x \]
\[ 55 - 45 = 0.45x \]
\[ 10 = 0.45x \]
\[ x = \frac{10}{0.45} = \frac{1000}{45} \approx 22.22 \text{ liters} \]

7. **Calculate the Percentage of Water Added**:
The percentage of water added to the original mixture is:
\[ \text{Percentage of Water Added} = \frac{x}{100} \times 100 = \frac{22.22}{100} \times 100 \approx 22.22\% \]

### Final Answer:
To reverse the proportion of milk and water, approximately **22.22%** of water should be added to the mixture.