An article is sold at a profit of 50%. If the cost price is doubled and the selling price is halved, then what will be the new profit or loss percentage

Options

A. 62.5 loss
B. 62.5 Profit
C. 37.5 loss
D. 37.5 Profit

Answer

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

### Step 1: Determine the Original Cost Price and Selling Price
Let's assume the cost price (CP) of the article is ₹100.

Since the article is sold at a profit of 50%, we can calculate the selling price (SP) as follows:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
\[ \text{Profit} = 50\% \text{ of CP} = 0.5 \times 100 = ₹50 \]
\[ \text{SP} = 100 + 50 = ₹150 \]

### Step 2: Adjust the Cost Price and Selling Price
According to the problem, the cost price is doubled and the selling price is halved.

New Cost Price (CP'):
\[ \text{New CP} = 2 \times \text{Original CP} = 2 \times 100 = ₹200 \]

New Selling Price (SP'):
\[ \text{New SP} = \frac{1}{2} \times \text{Original SP} = \frac{1}{2} \times 150 = ₹75 \]

### Step 3: Calculate the New Profit or Loss
Now, we need to find out if there is a profit or loss with the new cost price and selling price.

\[ \text{New Profit or Loss} = \text{New SP} - \text{New CP} = 75 - 200 = -₹125 \]

Since the result is negative, it indicates a loss.

### Step 4: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{New CP}}\right) \times 100 \]
\[ \text{Loss Percentage} = \left(\frac{125}{200}\right) \times 100 = 62.5\% \]

### Final Answer
The new profit or loss percentage is a **62.5% loss**.

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