The marked price of an item is ₹ 900 but a retailer purchases it on 40% discount and sells it on ₹ 900. The percentage profit of the retailer is:

Options

A. a) `60%`
B. b) `68(1)/(3)%`
C. c) `40%`
D. d) `66(2)/(3)%`

Answer

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

1. **Identify the Marked Price (MP)**:
The marked price of the item is given as ₹900.

2. **Calculate the Discount**:
The retailer purchases the item at a 40% discount.
\[ \text{Discount} = \frac{40}{100} \times \text{MP} = \frac{40}{100} \times 900 = 360 \]

3. **Calculate the Cost Price (CP)**:
The cost price is the marked price minus the discount.
\[ \text{CP} = \text{MP} - \text{Discount} = 900 - 360 = 540 \]

4. **Identify the Selling Price (SP)**:
The retailer sells the item for ₹900, which is the selling price.
\[ \text{SP} = 900 \]

5. **Calculate the Profit**:
Profit is calculated as the selling price minus the cost price.
\[ \text{Profit} = \text{SP} - \text{CP} = 900 - 540 = 360 \]

6. **Calculate the Profit Percentage**:
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{360}{540} \right) \times 100 = \left( \frac{2}{3} \right) \times 100 = 66.67\% \]

7. **Final Result**:
The percentage profit of the retailer is \(66 \frac{2}{3}\%\).