A shopkeeper sells one-third of his goods at a profit of 10%, another one-third at a profit of 20%, and the rest at a loss of 6%.What is his overall profit

Options

A. A. 8%
B. B. 4%
C. C. 20%
D. D. 3%

Explanation

To find the overall profit of the shopkeeper, we can break down the problem step by step.

### Step 1: Define the total cost of goods
Let's assume the total cost of the goods the shopkeeper has is \( C \). For simplicity, we can assume \( C = 300 \) rupees.

### Step 2: Calculate the cost of each segment of goods
Since the shopkeeper sells his goods in three equal parts, we can calculate the cost for each segment:
- One-third of goods: \( \frac{C}{3} = \frac{300}{3} = 100 \) rupees
- Another one-third of goods: \( \frac{C}{3} = 100 \) rupees
- The last one-third of goods: \( \frac{C}{3} = 100 \) rupees

### Step 3: Calculate the selling price for each segment
1. **First segment (10% profit)**:
- Cost: 100 rupees
- Selling Price = Cost + Profit = \( 100 + (10\% \text{ of } 100) = 100 + 10 = 110 \) rupees

2. **Second segment (20% profit)**:
- Cost: 100 rupees
- Selling Price = Cost + Profit = \( 100 + (20\% \text{ of } 100) = 100 + 20 = 120 \) rupees

3. **Third segment (6% loss)**:
- Cost: 100 rupees
- Selling Price = Cost - Loss = \( 100 - (6\% \text{ of } 100) = 100 - 6 = 94 \) rupees

### Step 4: Calculate the total selling price
Now, we can find the total selling price of all segments:
- Total Selling Price = Selling Price of First Segment + Selling Price of Second Segment + Selling Price of Third Segment
- Total Selling Price = \( 110 + 120 + 94 = 324 \) rupees

### Step 5: Calculate the overall profit
To find the overall profit, we subtract the total cost from the total selling price:
- Overall Profit = Total Selling Price - Total Cost
- Overall Profit = \( 324 - 300 = 24 \) rupees

### Conclusion
The overall profit of the shopkeeper is **24 rupees**.

---