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:

Options

A. 0.51
B. 0.49
C. 12 `3/4` %
D. 24 `1/2` %

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Assume the Cost Price (CP)
Let's assume the Cost Price (CP) of the article is Rs 100.

**Hint:** Start by assuming a simple value for CP to make calculations easier.

### Step 2: Define the Selling Price (SP)
Let the Selling Price (SP) of the article be Rs x.

**Hint:** Use a variable (x) to represent the unknown SP.

### Step 3: Understand the Loss Condition
According to the problem, if the article is sold at half of the previous selling price (which is x/2), there is a loss of 25.5% (which can be expressed as 25 1/2% or 51/2%).

**Hint:** Remember that a loss percentage indicates that the selling price is less than the cost price.

### Step 4: Set Up the Loss Equation
The formula for loss percentage is given by:
\[ \text{Loss Percentage} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]
Substituting the values we have:
\[ 25.5 = \frac{100 - \frac{x}{2}}{100} \times 100 \]

**Hint:** Rearranging the loss percentage formula will help you find the relationship between CP and SP.

### Step 5: Simplify the Equation
We can simplify the equation:
\[ 25.5 = 100 - \frac{x}{2} \]
Rearranging gives:
\[ \frac{x}{2} = 100 - 25.5 \]
\[ \frac{x}{2} = 74.5 \]
Multiplying both sides by 2:
\[ x = 149 \]

**Hint:** Isolate the variable x to find the selling price.

### Step 6: Calculate the Profit Percentage
Now that we have the Selling Price (SP) as Rs 149, we can calculate the profit percentage using the formula:
\[ \text{Profit Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \frac{149 - 100}{100} \times 100 \]
\[ \text{Profit Percentage} = \frac{49}{100} \times 100 = 49\% \]

**Hint:** Use the profit formula to find out how much profit you made compared to the cost price.

### Final Answer
The profit after selling the article at the previous selling price is **49%**.

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