On the basis of selling price of an article, the loss is calculated to be 25%. The percentage of loss on the basis of cost price is

Options

A. 18
B. 20
C. 22
D. 25

Answer

To solve the problem step by step, we will determine the percentage of loss based on the cost price when the loss is given as 25% based on the selling price.

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss
The formula for selling price when there is a loss is:
\[ \text{SP} = \text{CP} - \text{Loss} \]

### Step 2: Define the Selling Price and Loss
According to the problem, the loss is 25% of the selling price. Let's assume the selling price (SP) is 100. Therefore, the loss can be calculated as:
\[ \text{Loss} = 25\% \text{ of SP} = 25\% \text{ of } 100 = 25 \]

### Step 3: Calculate the Cost Price
Now, we can find the cost price (CP) using the selling price and the loss:
\[ \text{CP} = \text{SP} + \text{Loss} \]
Substituting the values we have:
\[ \text{CP} = 100 + 25 = 125 \]

### Step 4: Calculate the Loss Percentage based on Cost Price
Now that we have both the selling price and the cost price, we can calculate the loss percentage based on the cost price using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{25}{125} \right) \times 100 \]

### Step 5: Simplify the Calculation
Now, we simplify the fraction:
\[ \frac{25}{125} = \frac{1}{5} \]
Then, we multiply by 100:
\[ \text{Loss Percentage} = \frac{1}{5} \times 100 = 20\% \]

### Final Answer
The percentage of loss on the basis of cost price is **20%**.

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