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To solve the given problem, let's define the terms and use the formulas related to profit and loss:

### Problem Statement:
A man wanted to sell an article with a 20% profit, but he actually sold it at a 20% loss for Rs 480. At what price (Rs) did he want to sell it to earn the profit?

### Solution:
1. Let the cost price (CP) of the article be \( x \).

2. The article was sold at a 20% loss, so the selling price (SP) at 20% loss is:
   \[
   SP = x - 0.20x = 0.80x
   \]

3. According to the problem, the SP at 20% loss is Rs 480:
   \[
   0.80x = 480
   \]

4. Solving for \( x \):
   \[
   x = \frac{480}{0.80} = 600
   \]

5. To find the price at which he wanted to sell it for a 20% profit:
   \[
   \text{Desired SP} = x + 0.20x = 1.20x
   \]

6. Substituting \( x = 600 \):
   \[
   \text{Desired SP} = 1.20 \times 600 = 720
   \]

### Answer:
The price at which he wanted to sell it to earn the profit is **Rs 720**.

Would you like to go over any details or have any questions? Here are some related questions you might be interested in:

1. How is the cost price calculated in different profit and loss scenarios?
2. What formulas are used for calculating profit percentages?
3. How would the solution change if the selling price was given for a different loss percentage?
4. What happens if multiple transactions with different profit and loss percentages occur?
5. How can we adjust the selling price to meet specific profit targets?

**Tip:** Always identify the cost price first in profit and loss problems; it’s the key to solving them!

A man wanted to sell an article with 20% profit; but he actually sold at 20% loss for Rs 480. At what price (Rs) he wanted to sell it to earn the profit?

Find out how to determine the selling price of an article to achieve a 20% profit after it was sold at a 20% loss for Rs 480. This solution covers key concepts like profit and loss, percentage calculations, and basic algebra. Suitable for students in Grades 6-8.

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