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To solve this problem, let's break it down step-by-step.

### Problem Summary:
1. Arun bought 38 kg of rice for ₹1,710.
2. He sold the rice at a profit equal to the selling price of 8 kg of rice.
3. We need to find the selling price of 5 kg of rice.

### Solution:
1. **Find the Cost Price per kg of Rice:**

   The total cost for 38 kg is ₹1,710.
   \[
   \text{Cost Price per kg} = \frac{1710}{38} = 45 \, \text{₹/kg}
   \]

2. **Calculate the Selling Price per kg based on the Profit Condition:**

   Let the Selling Price per kg be \( x \).

   Since the profit is equal to the selling price of 8 kg of rice, we can write the profit as:
   \[
   \text{Profit} = 8x
   \]

   Now, using the profit formula:
   \[
   \text{Profit} = \text{Total Selling Price} - \text{Total Cost Price}
   \]
   
   Substitute the values:
   \[
   8x = 38x - 1710
   \]

3. **Solve for \( x \):**
   \[
   8x - 38x = -1710
   \]
   \[
   -30x = -1710
   \]
   \[
   x = \frac{1710}{30} = 57 \, \text{₹/kg}
   \]

4. **Calculate the Selling Price of 5 kg of Rice:**

   If the Selling Price per kg is ₹57, then the Selling Price for 5 kg is:
   \[
   5 \times 57 = 285 \, \text{₹}
   \]

### Answer:
The selling price of 5 kg of rice is **₹285**.

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Would you like a detailed breakdown or have any further questions?

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Here are five related questions for practice:
1. What would the selling price be if the profit was equivalent to 10 kg of rice's selling price instead of 8 kg?
2. If Arun bought 50 kg of rice instead of 38 kg, how would the selling price per kg change?
3. How much profit did Arun actually make in this transaction?
4. If the cost price per kg was higher, say ₹50 per kg, how would the selling price per kg change?
5. What is the total profit percentage Arun made on the transaction?

**Tip:** Remember that in profit problems, understanding the relationship between cost price, selling price, and profit percentage is key to finding solutions efficiently.

Arun bought 38 kg of rice for ₹1,710. He sold it at a profit equal to the selling price of 8 kg of rice. What is the selling price of 5 kg of rice?

Learn how to calculate the selling price of 5 kg of rice given that Arun bought 38 kg for ₹1,710 and sold it at a profit equal to the selling price of 8 kg of rice. This problem involves concepts of profit and loss, basic algebra, and unit price calculations, making it suitable for students in Grades 7-9.

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