If the cost price of 10 articles is equal to the selling price of 15 articles, then what is the loss percentage?

Options

A. a)`25%`
B. b)`50%`
C. c)`33.33%`
D. d)`20%`

Answer

To find the loss percentage when the cost price of 10 articles is equal to the selling price of 15 articles, we can follow these steps:

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let the cost price of one article be \( CP \).
Then, the cost price of 10 articles is \( 10 \times CP = 10CP \).

Let the selling price of one article be \( SP \).
Then, the selling price of 15 articles is \( 15 \times SP = 15SP \).

### Step 2: Set up the equation
According to the problem, the cost price of 10 articles is equal to the selling price of 15 articles:
\[ 10CP = 15SP \]

### Step 3: Find the ratio of CP to SP
To find the ratio of the cost price to the selling price, we can rearrange the equation:
\[ \frac{CP}{SP} = \frac{15}{10} \]
Simplifying this gives:
\[ \frac{CP}{SP} = \frac{3}{2} \]

### Step 4: Express SP in terms of CP
From the ratio, we can express \( SP \) in terms of \( CP \):
\[ SP = \frac{2}{3} CP \]

### Step 5: Calculate the loss
Loss occurs when the selling price is less than the cost price. The loss can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the value of \( SP \):
\[ \text{Loss} = CP - \frac{2}{3} CP = \frac{1}{3} CP \]

### Step 6: 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:
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{3} CP}{CP} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
The loss percentage is **33.33%**.

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