If cost price of 5 articles is equal to selling price of 8 articles then find the profit or loss percentage?

Options

A. 25.5% loss
B. 35% profit
C. 37.5% loss
D. 40% profit

Answer

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

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We are given that the cost price of 5 articles is equal to the selling price of 8 articles. This can be expressed mathematically as:
\[ \text{CP of 5 articles} = \text{SP of 8 articles} \]

### Step 2: Define the variables
Let the cost price of one article be \( k \). Therefore, the cost price of 5 articles will be:
\[ \text{CP} = 5k \]
Let the selling price of one article be \( m \). Therefore, the selling price of 8 articles will be:
\[ \text{SP} = 8m \]

### Step 3: Set up the equation
From the information given, we can set up the equation:
\[ 5k = 8m \]

### Step 4: Find the ratio of Cost Price to Selling Price
To find the profit or loss percentage, we need to find the ratio of the cost price to the selling price:
\[ \frac{\text{CP}}{\text{SP}} = \frac{5k}{8m} \]

### Step 5: Express Selling Price in terms of Cost Price
From the equation \( 5k = 8m \), we can express \( m \) in terms of \( k \):
\[ m = \frac{5k}{8} \]

Now substitute this back into the ratio:
\[ \frac{\text{CP}}{\text{SP}} = \frac{5k}{8 \times \frac{5k}{8}} = \frac{5k}{5k} = 1 \]

### Step 6: Determine Profit or Loss
Since the cost price is greater than the selling price, we can say that there is a loss. To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]

### Step 7: Calculate the Loss
Substituting the values:
1. We already know \( \text{CP} = 5k \) and \( \text{SP} = 8m = 5k \).
2. Thus, the loss is:
\[ \text{Loss} = 5k - 8m = 5k - 5k = 3k \]

Now substituting into the loss percentage formula:
\[ \text{Loss Percentage} = \frac{3k}{8k} \times 100 = \frac{3}{8} \times 100 = 37.5\% \]

### Final Answer
The loss percentage is \( 37.5\% \).

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