A milkman procures milk at the rate of Rs. `4cdot50` per litre and sells it to his customers at the same rate. If he makes a profit of `12 1/2%` the quantity of water he mixes for every litre of milk is-

Options

A. 50 ml
B. 100 ml
C. 125 ml
D. 175 ml

Answer

To solve the problem step by step, we need to determine how much water the milkman mixes with each litre of milk to achieve a profit of 12.5% while selling the milk at the same rate he procures it.

### Step-by-Step Solution:

1. **Understanding the Cost Price and Selling Price**:
- The milkman procures milk at the rate of Rs. 4.50 per litre.
- He sells the milk at the same rate of Rs. 4.50 per litre.

2. **Calculating the Profit Percentage**:
- The profit percentage is given as 12.5%.
- To convert this percentage into a fraction, we can express 12.5% as:
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]

3. **Understanding the Profit in Terms of Milk and Water**:
- If the milkman is making a profit of 12.5%, it means that for every 8 litres of the mixture (milk + water), he is selling it as if it were 8 litres of milk.
- This implies that he is mixing 1 litre of water with 8 litres of milk to achieve this profit.

4. **Calculating the Total Volume of the Mixture**:
- The total volume of the mixture (milk + water) when he mixes 1 litre of water with 8 litres of milk is:
\[ 8 \text{ litres of milk} + 1 \text{ litre of water} = 9 \text{ litres of mixture} \]

5. **Finding the Quantity of Water in 1 Litre of Milk**:
- To find out how much water he mixes for every litre of milk, we can set up a ratio:
\[ \text{Water in 1 litre of milk} = \frac{1 \text{ litre of water}}{8 \text{ litres of milk}} = \frac{1}{8} \text{ litre of water} \]

6. **Converting Litres to Millilitres**:
- Since we need the answer in millilitres, we convert \(\frac{1}{8}\) litre to millilitres:
\[ \frac{1}{8} \text{ litre} = \frac{1}{8} \times 1000 \text{ ml} = 125 \text{ ml} \]

### Final Answer:
The quantity of water he mixes for every litre of milk is **125 ml**.