A man gains `80%` by selling an article for a certain price. If he sells it at half the price, then what will be the loss percentage?

Options

A. 10
B. 15
C. 20
D. 40

Answer

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

### Step 1: Understand the Gain Percentage
The man gains 80% by selling an article. This means if the cost price (CP) of the article is Rs 100, then the selling price (SP) can be calculated as follows:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where Gain is 80% of CP.

### Step 2: Calculate the Selling Price
Given that the cost price (CP) is Rs 100:
\[ \text{Gain} = 80\% \text{ of } 100 = \frac{80}{100} \times 100 = Rs 80 \]
Now, calculate the selling price (SP):
\[ \text{SP} = 100 + 80 = Rs 180 \]

### Step 3: Selling at Half the Price
If the man sells the article at half the selling price:
\[ \text{New SP} = \frac{180}{2} = Rs 90 \]

### Step 4: Calculate the Loss
Now, we need to find out the loss incurred when selling at Rs 90. The loss can be calculated as:
\[ \text{Loss} = \text{CP} - \text{New SP} = 100 - 90 = Rs 10 \]

### Step 5: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{10}{100} \right) \times 100 = 10\% \]

### Final Answer
The loss percentage when the article is sold at half the price is **10%**.

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