A manufacturer marks his goods at 30% above the cost price. He allows a discount of 10% for cash customers and 15% for credit customers. 2/5 of the goods are sold for cash and the rest on credit. What is the percentage of profit or loss, when all the goods are sold?

Options

A. 7.5% Profit
B. 13.1% Profit
C. 6.3% Loss
D. 8% Loss

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price (CP)
Let the cost price of the goods be \( CP = 500 \) rupees.

### Step 2: Calculate the Marked Price (MP)
The manufacturer marks his goods at 30% above the cost price.
\[ MP = CP + 30\% \text{ of } CP \]
\[ MP = 500 + 0.30 \times 500 \]
\[ MP = 500 + 150 = 650 \text{ rupees} \]

### Step 3: Calculate Selling Price for Cash Customers
2/5 of the goods are sold for cash.
The total selling price for cash customers is:
\[ \text{Selling Price for Cash} = \frac{2}{5} \times MP \]
\[ \text{Selling Price for Cash} = \frac{2}{5} \times 650 = 260 \text{ rupees} \]

Now, calculate the selling price after the 10% discount:
\[ \text{Discount} = 10\% \text{ of } 260 = 0.10 \times 260 = 26 \text{ rupees} \]
\[ \text{Selling Price after Discount} = 260 - 26 = 234 \text{ rupees} \]

### Step 4: Calculate Selling Price for Credit Customers
The remaining goods (3/5) are sold on credit:
\[ \text{Selling Price for Credit} = \frac{3}{5} \times MP \]
\[ \text{Selling Price for Credit} = \frac{3}{5} \times 650 = 390 \text{ rupees} \]

Now, calculate the selling price after the 15% discount:
\[ \text{Discount} = 15\% \text{ of } 390 = 0.15 \times 390 = 58.5 \text{ rupees} \]
\[ \text{Selling Price after Discount} = 390 - 58.5 = 331.5 \text{ rupees} \]

### Step 5: Calculate Total Selling Price (SP)
Now, add the selling prices from cash and credit sales:
\[ \text{Total SP} = \text{Selling Price for Cash} + \text{Selling Price for Credit} \]
\[ \text{Total SP} = 234 + 331.5 = 565.5 \text{ rupees} \]

### Step 6: Calculate Profit
Now, calculate the profit:
\[ \text{Profit} = \text{Total SP} - CP \]
\[ \text{Profit} = 565.5 - 500 = 65.5 \text{ rupees} \]

### Step 7: Calculate Profit Percentage
Finally, calculate the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{65.5}{500} \right) \times 100 = 13.1\% \]

### Conclusion
The percentage of profit when all the goods are sold is **13.1%**.

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