A dealer sells goods at 4% loss on cost price but he uses 28 g instead of 32g.What is his percent profit or loss?

Options

A. `9(5)/(7)%` gain
B. `14(3)/(7)%` gain
C. `16(3)/(7)%` gain
D. `16(3)/(7)% ` gain

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Given Information
- The dealer sells goods at a 4% loss on the cost price (CP).
- He uses 28 grams instead of 32 grams.

### Step 2: Assume a Selling Price
Let's assume the selling price of 1 gram of the goods is 1 rupee. Therefore:
- Cost Price (CP) of 28 grams = 28 rupees
- Cost Price (CP) of 32 grams = 32 rupees

### Step 3: Calculate the Selling Price with Loss
Since the dealer claims to sell at a 4% loss on the cost price of 32 grams:
- Loss Percentage = 4%
- Selling Price (SP) of 32 grams = CP of 32 grams - Loss
- SP = 32 - (4% of 32)
- SP = 32 - (4/100 * 32) = 32 - 1.28 = 30.72 rupees

### Step 4: Find the Selling Price for 28 grams
The dealer sells 28 grams but claims it is 32 grams. Therefore, the selling price for 28 grams is also 30.72 rupees.

### Step 5: Calculate the Profit or Loss
Now we need to find the profit or loss when selling 28 grams:
- CP of 28 grams = 28 rupees
- SP of 28 grams = 30.72 rupees

Profit = SP - CP = 30.72 - 28 = 2.72 rupees

### Step 6: Calculate the Profit Percentage
Profit Percentage = (Profit / CP) * 100
- Profit = 2.72 rupees
- CP = 28 rupees

Profit Percentage = (2.72 / 28) * 100 = 9.71%

### Final Answer
The dealer's profit percentage is approximately **9.71%**.

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