A shopkeeper sells milk which contains 5% water. What quantity of pure milk should be added to 2 liters of milk (containing 5% water) so that the proportion of water becomes 4% ?

Options

A. 100ml
B. 250ml
C. 400ml
D. None of these

Answer

To solve the problem of how much pure milk should be added to 2 liters of milk containing 5% water to reduce the water content to 4%, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the amount of water in the initial milk:**
- The initial milk contains 5% water.
- For 2 liters of milk, the amount of water is:
\[ \text{Water} = 5\% \text{ of } 2 \text{ liters} = \frac{5}{100} \times 2 = 0.1 \text{ liters} \]

2. **Determine the amount of pure milk to be added:**
- Let \( x \) be the amount of pure milk (in liters) to be added.
- After adding \( x \) liters of pure milk, the total volume of the mixture will be \( 2 + x \) liters.
- The amount of water in the new mixture remains 0.1 liters since pure milk contains no water.

3. **Set up the equation for the new percentage of water:**
- We want the new percentage of water to be 4%. Therefore, we can set up the equation:
\[ \frac{0.1}{2 + x} = 4\% \]
- Converting 4% to a fraction gives us:
\[ \frac{0.1}{2 + x} = \frac{4}{100} \]

4. **Cross-multiply to solve for \( x \):**
- Cross-multiplying gives:
\[ 0.1 \times 100 = 4 \times (2 + x) \]
\[ 10 = 8 + 4x \]

5. **Isolate \( x \):**
- Rearranging the equation:
\[ 10 - 8 = 4x \]
\[ 2 = 4x \]
\[ x = \frac{2}{4} = 0.5 \text{ liters} \]

6. **Convert to milliliters (if necessary):**
- Since \( 1 \text{ liter} = 1000 \text{ ml} \):
\[ 0.5 \text{ liters} = 0.5 \times 1000 = 500 \text{ ml} \]

### Final Answer:
- The quantity of pure milk that should be added is **0.5 liters** or **500 ml**.