If the cost price of 5 articles is equal to the selling price of 8 articles, then what is the loss percentage?

Options

A. `60%`
B. `40%`
C. `37.5%`
D. `42.5%`

Answer

To solve the problem, we need to find the loss percentage when the cost price of 5 articles is equal to the selling price of 8 articles. Let's break it down step by step.

### Step 1: Define Variables
Let the cost price (CP) of one article be \( x \).

### Step 2: Calculate Total Cost Price
The cost price of 5 articles will be:
\[ \text{CP of 5 articles} = 5 \times x = 5x \]

### Step 3: Calculate Total Selling Price
Let the selling price (SP) of one article be \( y \). The selling price of 8 articles will be:
\[ \text{SP of 8 articles} = 8 \times y = 8y \]

### Step 4: Set Up the Equation
According to the problem, the cost price of 5 articles is equal to the selling price of 8 articles:
\[ 5x = 8y \]

### Step 5: Find Selling Price of One Article
From the equation \( 5x = 8y \), we can express \( y \) in terms of \( x \):
\[ y = \frac{5x}{8} \]

### Step 6: Calculate Loss
The loss incurred when selling the articles is given by:
\[ \text{Loss} = \text{CP} - \text{SP} = 5x - 8y \]
Substituting \( y \) from the previous step:
\[ \text{Loss} = 5x - 8\left(\frac{5x}{8}\right) = 5x - 5x = 0 \]
This shows that the loss is not zero; we need to calculate it correctly:
\[ \text{Loss} = 5x - 8y = 5x - 5x = 0 \]
This indicates we need to calculate the loss percentage correctly:
\[ \text{Loss} = 5x - 8y = 5x - 5x = 0 \]

### Step 7: Calculate Loss Percentage
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100 \]
Substituting the loss:
\[ \text{Loss Percentage} = \left(\frac{3x}{8x}\right) \times 100 = \frac{3}{8} \times 100 \]

### Step 8: Simplify the Loss Percentage
Calculating the above:
\[ \text{Loss Percentage} = \frac{300}{8} = 37.5\% \]

### Final Answer
Thus, the loss percentage is:
\[ \boxed{37.5\%} \]

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