A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000 gm for 800 gm. What is his net profit percentage?

Options

A. `57.5%`
B. `63.5%`
C. `42.5%`
D. `36.5%`

Answer

To find the net profit percentage of the shopkeeper, we will break down the problem into several steps:

### Step 1: Determine the Cost Price (CP)
Let the cost price of 1 kg (1000 grams) of goods be Rs 100.

### Step 2: Calculate the Effective Cost Price (ECP)
Since the shopkeeper uses a faulty balance that reads 1000 grams for 800 grams, the actual cost price for 800 grams is:
\[ \text{Actual Cost Price for 800g} = \frac{800}{1000} \times 100 = Rs 80 \]

### Step 3: Calculate the Marked Price (MP)
The shopkeeper marks up his goods by 40%. Therefore, the marked price (MP) for 1 kg is:
\[ \text{Marked Price} = \text{Cost Price} + 40\% \text{ of Cost Price} \]
\[ \text{Marked Price} = 100 + 0.40 \times 100 = 100 + 40 = Rs 140 \]

### Step 4: Calculate the Selling Price (SP) after Discount
The shopkeeper gives a discount of 10% on the marked price. Thus, the selling price (SP) is calculated as:
\[ \text{Selling Price} = \text{Marked Price} - 10\% \text{ of Marked Price} \]
\[ \text{Selling Price} = 140 - 0.10 \times 140 = 140 - 14 = Rs 126 \]

### Step 5: Calculate the Profit
Now, we can calculate the profit made by the shopkeeper:
\[ \text{Profit} = \text{Selling Price} - \text{Effective Cost Price} \]
\[ \text{Profit} = 126 - 80 = Rs 46 \]

### Step 6: Calculate the Profit Percentage
Finally, the profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Effective Cost Price}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{46}{80} \right) \times 100 = 57.5\% \]

### Final Answer:
The net profit percentage of the shopkeeper is **57.5%**.

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