A trader marks his goods at 35% above the cost price. He sells 80% the goods at the marked price and rest, he sells by allowing 35% discount on the marked price. His profit percent is:

Options

A. 27.55
B. 25.55
C. 20
D. 35

Answer

To find the profit percentage of the trader, let's break down the problem step by step:

### Step 1: Determine the Cost Price (CP) and Marked Price (MP)
Let the Cost Price (CP) of the goods be \( x \).

The trader marks his goods at 35% above the cost price:
\[ \text{Marked Price (MP)} = CP + 0.35 \times CP = 1.35 \times CP = 1.35x \]

### Step 2: Calculate the Selling Price (SP) for 80% of the Goods
The trader sells 80% of the goods at the marked price:
\[ \text{Selling Price for 80% of goods} = 0.80 \times \text{MP} = 0.80 \times 1.35x = 1.08x \]

### Step 3: Calculate the Selling Price (SP) for the Remaining 20% of the Goods
The remaining 20% of the goods are sold at a 35% discount on the marked price:
\[ \text{Discount on MP} = 0.35 \times \text{MP} = 0.35 \times 1.35x = 0.4725x \]
\[ \text{Selling Price after Discount} = \text{MP} - \text{Discount} = 1.35x - 0.4725x = 0.8775x \]
Now, for 20% of the goods:
\[ \text{Selling Price for 20% of goods} = 0.20 \times 0.8775x = 0.1755x \]

### Step 4: Calculate the Total Selling Price (SP)
Now, we sum the selling prices from both parts:
\[ \text{Total Selling Price (TSP)} = \text{SP from 80%} + \text{SP from 20%} = 1.08x + 0.1755x = 1.2555x \]

### Step 5: Calculate the Profit
Profit can be calculated as:
\[ \text{Profit} = \text{Total Selling Price} - \text{Cost Price} = 1.2555x - x = 0.2555x \]

### Step 6: Calculate the Profit Percentage
Profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{0.2555x}{x} \right) \times 100 = 25.55\% \]

### Final Answer
The profit percentage of the trader is **25.55%**.

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