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The problem involves profit and loss concepts. Let's break it down:

### Problem Statement:
An article is sold at a certain price. When sold at \(\frac{2}{3}\) of that price, the seller incurs a 10% loss. You are required to find the gain percentage when the article is sold at its original price.

### Let’s Solve:

1. **Let the Cost Price (C.P.) be 100 units** (for simplicity).
2. **Selling Price at \(\frac{2}{3}\) of the original price incurs a 10% loss**, which means the seller receives 90% of the cost price when selling at \(\frac{2}{3}\) of the original selling price.

   So, selling at \(\frac{2}{3}\) of the original selling price (S.P.) results in 90 units.

3. Let the original selling price be \(x\).

   \[
   \frac{2}{3}x = 90
   \]

   Solving for \(x\):

   \[
   x = 90 \times \frac{3}{2} = 135
   \]

4. So, the original selling price (S.P.) is 135 units.

5. Now, to find the **gain percentage**:
   \[
   \text{Gain Percentage} = \frac{\text{S.P.} - \text{C.P.}}{\text{C.P.}} \times 100
   \]
   \[
   = \frac{135 - 100}{100} \times 100 = 35\%
   \]

### Final Answer: The gain percentage is **35%**.

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Let me know if you need more details, or if you have any questions! Here are some related questions to expand your understanding:

1. How would the loss percentage change if the article were sold at half the original price?
2. What would be the new selling price if the seller wanted to make a 25% profit?
3. How do you calculate loss when selling below cost price?
4. If the cost price changes, how does that affect the gain or loss percentage?
5. Can the same method be applied to other percentage profit or loss problems?

**Tip:** Always assume simple numbers like 100 for cost price to simplify percentage problems involving profit and loss.

An article is sold at a certain price. By selling it at 2/3 of that price, one loses 10%. Find the gain per cent at the original price.

Solve a profit and loss problem where an article sold at 2/3 of its original price leads to a 10% loss. Learn how to calculate the gain percentage at the original price using simple algebra and percentage concepts. Suitable for students in Grades 8-10.

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