If the cost price of 15 articles be equal to the selling price of 20 articles, then find the loss % in the transaction.

Options

A. 0.16
B. 0.2
C. 0.25
D. 0.26

Explanation

To solve the problem step by step, we will follow the logic presented in the video transcript.

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

### Step 2: Calculate the Total Cost Price of 15 Articles
The cost price of 15 articles is:
\[ \text{Total CP} = 15 \times x = 15x \]

### Step 3: Calculate the Total Selling Price of 20 Articles
Let the selling price (SP) of one article be \( y \). The selling price of 20 articles is:
\[ \text{Total SP} = 20 \times y = 20y \]

### Step 4: Set Up the Equation
According to the problem, the cost price of 15 articles is equal to the selling price of 20 articles:
\[ 15x = 20y \]

### Step 5: Rearrange the Equation to Find the Ratio of SP to CP
We can rearrange the equation to find the ratio of SP to CP:
\[ \frac{SP}{CP} = \frac{15x}{20y} \]
This simplifies to:
\[ \frac{SP}{CP} = \frac{15}{20} = \frac{3}{4} \]

### Step 6: Find the Loss
The loss can be calculated using the formula:
\[ \text{Loss} = CP - SP \]
From the ratio, we know:
\[ SP = \frac{3}{4} CP \]
Thus, substituting this into the loss formula gives:
\[ \text{Loss} = CP - \frac{3}{4} CP = \frac{1}{4} CP \]

### Step 7: Calculate the Loss Percentage
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]
Substituting the loss we found:
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{4} CP}{CP} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Final Answer
The loss percentage in the transaction is **25%**.

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