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. data insufficient

Answer

To solve the problem step by step, we need to analyze the information provided and use the concept of alligation to find the price of the refined oil.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Quantity of refined oil (first oil) = 40 kg
- Price of vegetable oil (second oil) = Rs. 60 per kg
- Gain from selling the mixture = Rs. 10

2. **Assume the Price of Refined Oil:**
- Let the price of refined oil be Rs. y per kg.

3. **Calculate the Selling Price of the Mixture:**
- Since the shopkeeper gains Rs. 10 after selling the mixture, we need to find the cost price of the mixture first.
- The selling price of the mixture can be expressed as:
\[ \text{Selling Price} = \text{Cost Price} + \text{Gain} \]

4. **Find the Cost Price of the Mixture:**
- The cost price of the mixture is the sum of the cost prices of both oils:
\[ \text{Cost Price of Mixture} = (40 \times y) + (x \times 60) \]
- Here, \(x\) is the quantity of vegetable oil, which is not given.

5. **Calculate the Average Cost Price:**
- The average cost price of the mixture can be calculated if we know the total quantity, which is \(40 + x\).

6. **Set Up the Alligation:**
- We cannot find the average cost price since we do not have the quantity of vegetable oil (x). Therefore, we cannot apply the alligation method directly.

7. **Conclusion:**
- Since we do not have sufficient information to find the price of the refined oil, we conclude that the data is insufficient.

### Final Answer:
The correct answer is **Option 4: Data Insufficient**.