A trader marks-up his goods by 80% and gives discount of 25%. Besides it he weighs 10% less amount while selling his goods. What is the net profit of trader?

Options

A. 50%
B. 35%
C. 45%
D. 55%

Answer

To solve the problem step by step, we will calculate the net profit of the trader based on the given information.

### Step 1: Determine the Cost Price (CP)
Assume the cost price (CP) of 1000 grams of goods is ₹100.

### Step 2: Calculate the Marked Price (MP)
The trader marks up his goods by 80%.
- Marked Price (MP) = CP + (Markup Percentage × CP)
- MP = 100 + (80% of 100) = 100 + 80 = ₹180

**Hint:** Remember that the markup is added to the cost price to find the marked price.

### Step 3: Calculate the Selling Price (SP) after Discount
The trader gives a discount of 25% on the marked price.
- Discount = 25% of MP = 25% of 180 = (25/100) × 180 = ₹45
- Selling Price (SP) = MP - Discount = 180 - 45 = ₹135

**Hint:** Discounts reduce the marked price, so subtract the discount from the marked price to find the selling price.

### Step 4: Determine the Actual Quantity Sold
The trader weighs 10% less than the actual amount while selling.
- Actual Quantity = 1000 grams
- Quantity Sold = 1000 grams - (10% of 1000 grams) = 1000 - 100 = 900 grams

**Hint:** When calculating the quantity sold, remember to subtract the percentage of the total quantity that is not given.

### Step 5: Calculate the Cost Price of the Quantity Sold
Now, we need to find the cost price for the quantity actually sold (900 grams).
- Cost Price of 900 grams = (CP of 1000 grams / 1000) × 900 = (100 / 1000) × 900 = ₹90

**Hint:** To find the cost price for a different quantity, use the ratio of the quantities to the total cost price.

### Step 6: Calculate the Profit
Now, we can calculate the profit made by the trader.
- Profit = Selling Price - Cost Price of Quantity Sold
- Profit = 135 - 90 = ₹45

**Hint:** Profit is the difference between what you earn from selling and what you spent to acquire the goods.

### Step 7: Calculate the Profit Percentage
To find the profit percentage:
- Profit Percentage = (Profit / Cost Price of Quantity Sold) × 100
- Profit Percentage = (45 / 90) × 100 = 50%

**Hint:** Profit percentage tells you how much profit you made relative to your costs.

### Final Answer
The net profit percentage of the trader is **50%**.

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