A milkman makes 20% profit by selling milk mixed with water at Rs 9 per litre. If the cost price of 1 litre pure milk Is Rs 10, then the ratio of milk and water in the mixture is

Options

A. `3:1`
B. `4:1`
C. `3:2`
D. `4:3`

Answer

To find the ratio of milk and water in the mixture sold by the milkman, we can follow these steps:

### Step 1: Determine the Cost Price of the Mixture
The selling price (SP) of the milk mixture is given as Rs 9 per litre, and the milkman makes a profit of 20%.

To find the cost price (CP) of the mixture, we can use the formula for profit:
\[ SP = CP + Profit \]
Since profit is 20% of CP, we can express this as:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]
Thus, we can rearrange this to find CP:
\[ CP = \frac{SP}{1.2} = \frac{9}{1.2} = 7.5 \text{ Rs per litre} \]

### Step 2: Set Up the Allegation Method
Next, we will use the allegation method to find the ratio of milk to water.

1. The cost price of pure milk is Rs 10 per litre.
2. The cost price of water is Rs 0 (since it is free).
3. The cost price of the mixture is Rs 7.5 per litre.

### Step 3: Apply the Allegation Formula
We set up the allegation as follows:

- Write the price of milk (Rs 10) on one side.
- Write the price of water (Rs 0) on the other side.
- Write the price of the mixture (Rs 7.5) in the middle.

Now, we calculate the differences:

\[ \text{Difference between milk and mixture} = 10 - 7.5 = 2.5 \]
\[ \text{Difference between mixture and water} = 7.5 - 0 = 7.5 \]

### Step 4: Determine the Ratio
Now we can express the ratio of milk to water using the differences calculated:

\[ \text{Ratio of milk to water} = \frac{Difference \, of \, water}{Difference \, of \, milk} = \frac{7.5}{2.5} = 3:1 \]

### Conclusion
Thus, the ratio of milk to water in the mixture is **3:1**.

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