Selling price of 25 articles is equal to cost price of 20 articles. Find profit/loss %.

Options

A. 10%
B. 15%
C. 20%
D. 25%

Answer

To solve the problem step by step, we need to find the profit or loss percentage based on the given information.

### Step 1: Understand the relationship between Selling Price (SP) and Cost Price (CP)
We know that the selling price of 25 articles is equal to the cost price of 20 articles.

### Step 2: Set up the equations
Let the cost price of one article be \( CP \). Therefore, the cost price of 20 articles is:
\[ CP_{20} = 20 \times CP \]
Let the selling price of one article be \( SP \). Therefore, the selling price of 25 articles is:
\[ SP_{25} = 25 \times SP \]
According to the problem:
\[ SP_{25} = CP_{20} \]
This gives us the equation:
\[ 25 \times SP = 20 \times CP \]

### Step 3: Find the ratio of SP to CP
From the equation \( 25 \times SP = 20 \times CP \), we can rearrange it to find the ratio of SP to CP:
\[ \frac{SP}{CP} = \frac{20}{25} = \frac{4}{5} \]

### Step 4: Calculate the loss
Since \( SP < CP \), there is a loss. The loss can be calculated as:
\[ Loss = CP - SP \]
To express SP in terms of CP, we can write:
\[ SP = \frac{4}{5} CP \]
Thus, the loss becomes:
\[ Loss = CP - \frac{4}{5} CP = \frac{1}{5} CP \]

### Step 5: Calculate the percentage of loss
The percentage of loss is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{Loss}{CP} \right) \times 100 \]
Substituting the value of loss:
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{5} CP}{CP} \right) \times 100 = \left( \frac{1}{5} \right) \times 100 = 20\% \]

### Final Answer
The profit/loss percentage is:
\[ \text{Loss Percentage} = 20\% \]