The shopkeeper mixed 40 kg refined oil with vegetable oil worth rs 60 per kg. Thus he gains rs 10 after selling the mixture of the two oils. The price of the first oil is:

Options

A. 20
B. 25
C. 45
D. can't be determined

Answer

To solve the problem, we need to determine the price of the refined oil. Let's break it down step by step.

### Step 1: Understand the given information
- We have 40 kg of refined oil.
- The vegetable oil costs Rs. 60 per kg.
- The shopkeeper gains Rs. 10 after selling the mixture.

### Step 2: Establish variables
Let the price of the refined oil be \( x \) Rs per kg.

### Step 3: Calculate the total cost of the oils
- The cost of 40 kg of refined oil = \( 40 \times x = 40x \) Rs.
- The cost of the vegetable oil (assuming we mix it with some quantity) = \( 60y \) Rs, where \( y \) is the quantity of vegetable oil in kg.

### Step 4: Calculate the total cost of the mixture
The total cost of the mixture will be:
\[ \text{Total Cost} = \text{Cost of Refined Oil} + \text{Cost of Vegetable Oil} = 40x + 60y \]

### Step 5: Determine the selling price of the mixture
Let’s assume the selling price of the mixture is \( S \) Rs. Since the shopkeeper gains Rs. 10, we can express the selling price as:
\[ S = \text{Total Cost} + 10 = (40x + 60y) + 10 \]

### Step 6: Calculate the total quantity of the mixture
The total quantity of the mixture is:
\[ \text{Total Quantity} = 40 + y \]

### Step 7: Calculate the selling price per kg
The selling price per kg of the mixture is:
\[ \text{Selling Price per kg} = \frac{S}{\text{Total Quantity}} = \frac{(40x + 60y + 10)}{(40 + y)} \]

### Step 8: Set up the equation
Since the selling price per kg must equal the cost price per kg of the mixture, we can set up the equation:
\[ \frac{(40x + 60y + 10)}{(40 + y)} = \text{Cost Price per kg} \]

### Step 9: Solve for \( x \)
However, we notice that we do not have enough information to determine \( x \) without knowing the quantity \( y \) of vegetable oil used. Therefore, we conclude that the price of the refined oil cannot be determined with the given information.

### Conclusion
The price of the refined oil cannot be determined with the information provided.

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