The price of petrol is rs 60 per litre and the price of spirit is rs 40 per litre. In what ratio the petrol and spirit be mixed such that the profit after selling the mixture at rs 75 per litre be `25%?`

Options

A. 1:1
B. 3:2
C. 5:1
D. such a mixture is not possible

Answer

To solve the problem of mixing petrol and spirit to achieve a desired profit margin, we can follow these steps:

### Step 1: Determine the Cost Price of the Mixture
We need to find the cost price (CP) of the mixture that will allow us to achieve a 25% profit when sold at Rs. 75 per litre.

Given:
- Selling Price (SP) = Rs. 75 per litre
- Profit Percentage = 25%

To find the Cost Price (CP), we can use the formula:
\[ SP = CP + \text{Profit} \]
Where Profit can be calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]
Thus, we can rewrite the equation as:
\[ SP = CP + \frac{25}{100} \times CP = CP \left(1 + \frac{25}{100}\right) = CP \times 1.25 \]
Now, substituting the SP:
\[ 75 = CP \times 1.25 \]
To find CP, we rearrange the equation:
\[ CP = \frac{75}{1.25} = 60 \]

### Step 2: Set Up the Alligation
Now we know that the cost price of the mixture should be Rs. 60 per litre. We will use the alligation method to find the ratio of petrol and spirit.

- Cost Price of Petrol = Rs. 60 per litre
- Cost Price of Spirit = Rs. 40 per litre
- Cost Price of Mixture = Rs. 60 per litre

Using alligation, we set it up as follows:

\[ \text{Cost Price of Petrol} \quad \text{Cost Price of Mixture} \quad \text{Cost Price of Spirit} \]
\[ \text{(60)} \quad \quad \text{(60)} \quad \quad \text{(40)} \]

### Step 3: Calculate the Differences
Now, we calculate the differences:
- Difference between CP of Petrol and CP of Mixture:
\[ 60 - 60 = 0 \]
- Difference between CP of Spirit and CP of Mixture:
\[ 60 - 40 = 20 \]

### Step 4: Determine the Ratio
The ratio of petrol to spirit is given by the inverse of the differences calculated:
\[ \text{Ratio} = \frac{\text{Difference for Spirit}}{\text{Difference for Petrol}} = \frac{20}{0} \]

Since the difference for petrol is 0, it indicates that we need only spirit to achieve the desired mixture cost. Thus, the ratio of petrol to spirit is:
\[ \text{Petrol:Spirit} = 0:1 \]

### Final Answer
The petrol and spirit should be mixed in the ratio of **0:1**, meaning we only use spirit to achieve the desired profit.