Out of 100 articles 25 articles were sold at 25% profit and the remaining articles were sold at 25% loss. What will be the total loss percentage?

Options

A. `15`
B. `12.5`
C. `20`
D. `10`

Answer

To solve the problem step by step, we will calculate the total cost price (CP), total selling price (SP), and then find the total loss percentage.

### Step 1: Determine the Cost Price of the Articles
Assume the cost price (CP) of one article is \(4\) (this is an arbitrary value for easier calculation).

- Total CP for 100 articles = \(100 \times 4 = 400\)

### Step 2: Calculate Selling Price for Articles Sold at Profit
25 articles are sold at a 25% profit.

- Selling Price (SP) for one article sold at profit:
\[ SP = CP + (25\% \text{ of } CP) = 4 + (0.25 \times 4) = 4 + 1 = 5 \]

- Total SP for 25 articles:
\[ SP = 25 \times 5 = 125 \]

### Step 3: Calculate Selling Price for Articles Sold at Loss
The remaining articles are 75, which are sold at a 25% loss.

- Selling Price (SP) for one article sold at loss:
\[ SP = CP - (25\% \text{ of } CP) = 4 - (0.25 \times 4) = 4 - 1 = 3 \]

- Total SP for 75 articles:
\[ SP = 75 \times 3 = 225 \]

### Step 4: Calculate Total Selling Price
Now, we can find the total selling price for all articles.

- Total SP = SP from articles sold at profit + SP from articles sold at loss:
\[ Total SP = 125 + 225 = 350 \]

### Step 5: Calculate Total Loss
Now, we can calculate the total loss.

- Total Loss = Total CP - Total SP:
\[ Total Loss = 400 - 350 = 50 \]

### Step 6: Calculate Loss Percentage
Finally, we calculate the loss percentage.

- Loss Percentage = \(\frac{Total Loss}{Total CP} \times 100\):
\[ Loss Percentage = \frac{50}{400} \times 100 = 12.5\% \]

### Conclusion
The total loss percentage is **12.5%**.

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