A man purchases three type of item in ratio 2.3:4 and their cost price are Rs 300, Rs 500 and Rs 700 respectively. If he sold first second and third type of article at 10%, 5% and 4% profit respectively, then find his overall approximate profit percentage?

Options

A. A)`7%`
B. B)`2%`
C. C)`4%`
D. D)`5%`

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the number of items purchased
The items are purchased in the ratio of 2:3:4. We can denote the number of items as:
- First type: 2x
- Second type: 3x
- Third type: 4x

### Step 2: Calculate the total cost price for each type of item
The cost prices for each type of item are given as:
- First type: Rs 300
- Second type: Rs 500
- Third type: Rs 700

Now, we can calculate the total cost price (CP) for each type:
- Total CP for first type = Number of items × Cost price = 2x × 300 = 600x
- Total CP for second type = Number of items × Cost price = 3x × 500 = 1500x
- Total CP for third type = Number of items × Cost price = 4x × 700 = 2800x

### Step 3: Calculate the overall cost price
Now, we can sum up the total cost prices:
\[ \text{Total CP} = 600x + 1500x + 2800x = 4900x \]

### Step 4: Calculate the selling price for each type of item
The selling prices (SP) for each type of item can be calculated using the profit percentages:
- Selling price for first type = Cost price + Profit = 600x + (10% of 600x) = 600x + 60x = 660x
- Selling price for second type = Cost price + Profit = 1500x + (5% of 1500x) = 1500x + 75x = 1575x
- Selling price for third type = Cost price + Profit = 2800x + (4% of 2800x) = 2800x + 112x = 2912x

### Step 5: Calculate the overall selling price
Now, we can sum up the total selling prices:
\[ \text{Total SP} = 660x + 1575x + 2912x = 5147x \]

### Step 6: Calculate the overall profit
The overall profit can be calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} = 5147x - 4900x = 247x \]

### Step 7: Calculate the overall profit percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Total CP}}\right) \times 100 = \left(\frac{247x}{4900x}\right) \times 100 \]
\[ = \left(\frac{247}{4900}\right) \times 100 \approx 5.04\% \]

### Step 8: Conclusion
The overall approximate profit percentage is about 5%.