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 find the net profit percentage of the trader, we can follow these steps:

### Step 1: Determine the Cost Price (CP)
Let's assume the cost price of the goods is ₹100.

### Step 2: Calculate the Marked Price (MP)
The trader marks up his goods by 80%. Therefore, the marked price can be calculated as follows:
\[ \text{Marked Price} = \text{Cost Price} + \left(\frac{80}{100} \times \text{Cost Price}\right) = 100 + 80 = ₹180 \]

### Step 3: Calculate the Selling Price (SP) after Discount
The trader gives a discount of 25% on the marked price. Thus, the selling price can be calculated as:
\[ \text{Selling Price} = \text{Marked Price} - \left(\frac{25}{100} \times \text{Marked Price}\right) = 180 - 45 = ₹135 \]

### Step 4: Adjust for the Weight Reduction
The trader weighs 10% less when selling. Therefore, if he sells 90 grams instead of 100 grams, we need to calculate the effective selling price per gram:
\[ \text{Effective Selling Price per gram} = \frac{\text{Selling Price}}{\text{Actual Weight Sold}} = \frac{135}{90} = ₹1.5 \]

### Step 5: Calculate the Cost Price per gram
Since the cost price for 100 grams is ₹100, the cost price per gram is:
\[ \text{Cost Price per gram} = \frac{100}{100} = ₹1 \]

### Step 6: Calculate the Profit per gram
Now, we can find the profit per gram:
\[ \text{Profit per gram} = \text{Effective Selling Price per gram} - \text{Cost Price per gram} = 1.5 - 1 = ₹0.5 \]

### Step 7: Calculate the Profit Percentage
Finally, we can calculate the profit percentage based on the cost price:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit per gram}}{\text{Cost Price per gram}} \times 100\right) = \left(\frac{0.5}{1} \times 100\right) = 50\% \]

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

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