If the cost price of an article is `3/2` of its selling price, then the profit or loss per cent is

Options

A. `33 1/3` % profit
B. `33 1/3` % loss
C. `33 1/8`% loss
D. `33 1/8` % profit

Answer

To find the profit or loss percentage when the cost price (CP) of an article is \( \frac{3}{2} \) of its selling price (SP), we can follow these steps:

### Step 1: Define the relationship between CP and SP
Given that:
\[ CP = \frac{3}{2} \times SP \]

### Step 2: Express SP in terms of CP
From the equation above, we can express the selling price (SP) in terms of the cost price (CP):
\[ SP = \frac{2}{3} \times CP \]

### Step 3: Calculate Profit or Loss
To find out if there is a profit or loss, we need to compare CP and SP. Since \( CP > SP \) (because \( \frac{3}{2} > 1 \)), there is a loss.

### Step 4: Calculate the amount of loss
The loss can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting \( SP \) from Step 2:
\[ \text{Loss} = CP - \frac{2}{3} \times CP = CP \left(1 - \frac{2}{3}\right) = CP \left(\frac{1}{3}\right) \]

### Step 5: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]
Substituting the value of Loss from Step 4:
\[ \text{Loss Percentage} = \left(\frac{CP \left(\frac{1}{3}\right)}{CP}\right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
Thus, the profit or loss percent is:
\[ \text{Loss Percentage} = 33 \frac{1}{3} \% \]