A relailer gets a discount of 40% on the printed price of an article. The retailer sells it at the printed price. His gain per cent is

Options

A. `40%`
B. `55%`
C. `66(2)/(3)%`
D. `75%`

Answer

To solve the problem, we need to determine the gain percentage of the retailer when he sells the article at the printed price after receiving a discount of 40%.

Let's break it down step-by-step:

### Step 1: Define the Printed Price
Let the printed price of the article be \( P \).

### Step 2: Calculate the Discount Amount
The retailer receives a discount of 40% on the printed price. Therefore, the discount amount can be calculated as:
\[ \text{Discount} = 40\% \text{ of } P = \frac{40}{100} \times P = 0.4P \]

### Step 3: Calculate the Cost Price (CP)
The cost price for the retailer is the price he pays after the discount. Thus, the cost price can be calculated as:
\[ \text{Cost Price (CP)} = \text{Printed Price} - \text{Discount} = P - 0.4P = 0.6P \]

### Step 4: Selling Price (SP)
The retailer sells the article at the printed price, which is:
\[ \text{Selling Price (SP)} = P \]

### Step 5: Calculate the Gain
The gain can be calculated as:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = P - 0.6P = 0.4P \]

### Step 6: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{0.4P}{0.6P} \right) \times 100 = \left( \frac{0.4}{0.6} \right) \times 100 = \frac{40}{60} \times 100 = \frac{2}{3} \times 100 \approx 66.67\% \]

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

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