In what ratio should freely available water be mixed with the wine worth rs 60 per litre so that after selling the mixture at rs 50 per litre, the profit will be `25%`?

Options

A. 1:2
B. 2:3
C. 3:4
D. 4:5

Answer

To solve the problem of mixing freely available water with wine worth Rs 60 per litre to achieve a selling price of Rs 50 per litre with a profit of 25%, we can follow these steps:

### Step 1: Determine the selling price and profit percentage
We know that the selling price (SP) of the mixture is Rs 50 per litre and the desired profit percentage is 25%.

### Step 2: Calculate the cost price (CP) of the mixture
To find the cost price (CP) of the mixture, we can use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Since profit is 25% of CP, we can express this as:
\[ \text{SP} = \text{CP} + 0.25 \times \text{CP} = 1.25 \times \text{CP} \]
Substituting the SP value:
\[ 50 = 1.25 \times \text{CP} \]
To find CP, we rearrange the equation:
\[ \text{CP} = \frac{50}{1.25} = 40 \text{ Rs per litre} \]

### Step 3: Establish the ratio of wine to water
We know the cost price of the wine is Rs 60 per litre and the cost price of the mixture is Rs 40 per litre. We can set up the alligation method to find the ratio of wine to water.

- Cost of wine = Rs 60 (higher price)
- Cost of water = Rs 0 (since it is freely available)
- Cost of mixture = Rs 40 (lower price)

### Step 4: Apply the alligation rule
Using the alligation method:
- The difference between the cost of wine and the cost of mixture:
\[ 60 - 40 = 20 \]
- The difference between the cost of mixture and the cost of water:
\[ 40 - 0 = 40 \]

### Step 5: Calculate the ratio
The ratio of wine to water can be found by taking the differences calculated:
\[ \text{Ratio of wine to water} = \frac{40}{20} = 2:1 \]

### Conclusion
Thus, the ratio in which freely available water should be mixed with the wine is **2:1**.

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