The printed price of an article is Rs 900 but the retailer gets a discount of 40%. He sells the artice for Rs 900. Retailer's gain per cent is :

Options

A. `40%`
B. `60%`
C. `66(2)/(3)%`
D. `58(1)/(3)%`

Answer

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

### Step 1: Determine the Discount Amount
The printed price (marked price) of the article is Rs 900, and the retailer receives a discount of 40%.

To find the discount amount:
\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) \]
\[ \text{Discount} = 900 \times \left(\frac{40}{100}\right) = 900 \times 0.4 = 360 \]

### Step 2: Calculate the Cost Price
The cost price (CP) for the retailer is the marked price minus the discount:
\[ \text{Cost Price} = \text{Marked Price} - \text{Discount} \]
\[ \text{Cost Price} = 900 - 360 = 540 \]

### Step 3: Identify the Selling Price
The selling price (SP) of the article is given as Rs 900.

### Step 4: Calculate the Profit
Profit can be calculated by subtracting the cost price from the selling price:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
\[ \text{Profit} = 900 - 540 = 360 \]

### Step 5: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
\[ \text{Profit Percentage} = \left(\frac{360}{540}\right) \times 100 \]

Now, simplify the fraction:
\[ \frac{360}{540} = \frac{2}{3} \]
Thus,
\[ \text{Profit Percentage} = \left(\frac{2}{3}\right) \times 100 = \frac{200}{3} \approx 66.67\% \]

### Final Answer
The retailer's gain percentage is approximately 66.67%.

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