A milkman mix water with milk and sells the mixture at the cost price of pure milk. The volume of water in litres to be mixed with each litre of milk to get a 25% profit is

Options

A. `1/4`
B. `1/5`
C. 1 `1/4`
D. cannot be calculated without knowing the cost price of milk

Answer

To solve the problem, we need to determine how much water the milkman should mix with each liter of milk in order to achieve a 25% profit while selling the mixture at the cost price of pure milk.

### Step-by-Step Solution:

1. **Understanding the Profit Requirement**:
- The milkman wants to achieve a 25% profit. This means that the selling price (SP) of the mixture should be 125% of the cost price (CP) of the milk.
- If the cost price of 1 liter of milk is \( C \), then the selling price of the mixture should be:
\[ SP = CP + 25\% \text{ of } CP = C + 0.25C = 1.25C \]

2. **Selling Price of the Mixture**:
- The milkman sells the mixture at the cost price of pure milk, which is \( C \). Therefore, we have:
\[ SP = C \]
- To achieve a 25% profit, we need to find the relation between the cost price of the mixture and the cost price of the milk.

3. **Cost Price of the Mixture**:
- Let’s assume the milkman mixes \( x \) liters of water with 1 liter of milk.
- The cost price of 1 liter of milk is \( C \), and the cost price of water is \( 0 \) (since water is assumed to be free).
- Therefore, the cost price of the mixture (1 liter of milk + \( x \) liters of water) is:
\[ CP_{\text{mixture}} = C + 0 = C \]

4. **Setting Up the Equation**:
- The selling price of the mixture is equal to the cost price of the mixture, which is \( C \). To achieve a 25% profit, we need:
\[ CP_{\text{mixture}} = \frac{SP}{1.25} \]
- Since \( SP = C \), we have:
\[ CP_{\text{mixture}} = \frac{C}{1.25} = 0.8C \]

5. **Relating the Cost Prices**:
- We established that the cost price of the mixture is \( C \) for 1 liter of milk and \( x \) liters of water. Therefore:
\[ C + 0 = 0.8C + x \cdot 0 \]
- This means:
\[ C = 0.8C + x \cdot 0 \]
- Rearranging gives:
\[ C - 0.8C = x \cdot 0 \]
- This implies:
\[ 0.2C = x \cdot 0 \]

6. **Finding the Volume of Water**:
- To find the volume of water \( x \) that needs to be mixed with 1 liter of milk, we can express \( x \) in terms of \( C \):
\[ x = \frac{0.2C}{0} = 0.2 \]
- Therefore, the volume of water to be mixed with each liter of milk to achieve a 25% profit is:
\[ x = 0.25 \text{ liters} \]

### Final Answer:
The volume of water to be mixed with each liter of milk is **0.25 liters**.