A shopkeeper sells his articles in such a way that the selling price of 5 articles is equals to the cost price of 3 articles. Find his profit or loss percentage in that transaction.

Options

A. A)40% profit
B. B)40% loss
C. C)33.33 profit
D. D)33.33 loss

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between Selling Price (SP) and Cost Price (CP)
The problem states that the selling price of 5 articles is equal to the cost price of 3 articles. We can express this relationship mathematically.

### Step 2: Define variables for CP and SP
Let the cost price of one article be \( CP \) and the selling price of one article be \( SP \).

### Step 3: Set up the equation based on the relationship given
From the problem, we have:
\[ 5 \times SP = 3 \times CP \]

### Step 4: Express SP in terms of CP
To find the selling price in terms of the cost price, we can rearrange the equation:
\[ SP = \frac{3}{5} \times CP \]

### Step 5: Calculate the loss
Now, we can determine the loss incurred by the shopkeeper. The loss is calculated as:
\[ Loss = CP - SP \]
Substituting the value of SP from the previous step:
\[ Loss = CP - \frac{3}{5} \times CP = \frac{2}{5} \times CP \]

### Step 6: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ Loss\% = \left( \frac{Loss}{CP} \right) \times 100 \]
Substituting the value of Loss:
\[ Loss\% = \left( \frac{\frac{2}{5} \times CP}{CP} \right) \times 100 = \frac{2}{5} \times 100 = 40\% \]

### Step 7: Conclusion
The shopkeeper incurs a loss of 40%.

### Final Answer
The correct answer is 40% loss.

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