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The problem presented in the image is as follows:

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**Question 12:**

An article is sold at a certain price. If it is sold at half of the previous selling price, then there is a loss of \( 25 \frac{1}{2} \% \). The profit after selling the article at the previous selling price is:
- (1) 51%
- (2) 49%
- (3) \( 12 \frac{3}{4} \% \)
- (4) \( 24 \frac{1}{2} \% \)

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### Solution Outline:

1. **Understanding the Problem:**
   - Selling at half the previous price results in a loss of \( 25 \frac{1}{2} \% \).
   - This can be converted to a fractional value: \( 25 \frac{1}{2} \% = \frac{51}{2} \% = 0.255 \).

2. **Set the Selling Price:**
   Let the original selling price be \( S \). The selling price after reducing it by half is \( \frac{S}{2} \).

3. **Loss Definition:**
   - Loss percentage is defined as:
     \[
     \text{Loss \%} = \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100
     \]
   - Here, the loss is \( 25.5\% \), and the selling price after the loss is \( \frac{S}{2} \).

4. **Set up the Equation:**
   - If the loss is \( 25.5\% \), it means the article was sold at \( 74.5\% \) of the cost price, which means:
     \[
     \frac{S}{2} = 0.745 \times \text{Cost Price (C)}
     \]
   - Therefore, the cost price \( C \) can be expressed as:
     \[
     C = \frac{\frac{S}{2}}{0.745} = \frac{S}{1.49}
     \]

5. **Profit Calculation:**
   - The profit percentage when selling at the original price \( S \) is:
     \[
     \text{Profit \%} = \frac{S - C}{C} \times 100
     \]
   - Substituting \( C = \frac{S}{1.49} \):
     \[
     \text{Profit \%} = \frac{S - \frac{S}{1.49}}{\frac{S}{1.49}} \times 100
     \]
     Simplifying this expression, the profit percentage turns out to be approximately **49%**.

Hence, the correct answer is **option (2) 49%**.

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Would you like further details or clarification on any step?

Here are some related questions to enhance your understanding:

1. How do you calculate the cost price from a given selling price and loss percentage?
2. What is the relationship between cost price, selling price, profit, and loss?
3. How does a change in selling price impact the profit or loss percentage?
4. Can the same method be applied to calculate profit percentage if the selling price is increased instead of halved?
5. What happens to the profit percentage if the loss percentage is different, say 10% or 15%?

**Tip:** Always express percentages as decimals for easier calculations, and ensure you understand the relationship between cost price, selling price, and profit/loss percentages.

An article is sold at a certain price. If it is sold at half of the previous selling price, then there is a loss of 25 1/2%. The profit after selling the article at the previous selling price is:
(1) 51%
(2) 49%
(3) 12 3/4%
(4) 24 1/2%

Understand how to calculate profit percentage when an article sold at half price results in a 25.5% loss. Learn step-by-step how to derive the original profit, using core concepts such as percentage, loss, and selling price. Suitable for high school students studying commerce or business math.

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