A rice trader buys 8 quintals of rice for Rs. 3,600. 10 % rice is lost in transportation. At what rate should he sell to earn 15% profit?

Options

A. Rs.4600 per quintal
B. Rs. 517.5 per quintal
C. Rs. 575 per quintal
D. Rs. 582.3 per quintal

Answer

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

### Step 1: Calculate the Cost Price (CP) per quintal
The total cost price for 8 quintals of rice is Rs. 3600.

\[ \text{Cost Price per quintal} = \frac{\text{Total Cost Price}}{\text{Total Quintals}} = \frac{3600}{8} = 450 \text{ Rs. per quintal} \]

**Hint:** To find the cost price per unit, divide the total cost by the total quantity.

### Step 2: Calculate the quantity of rice after loss
10% of the rice is lost during transportation. Therefore, the quantity of rice that is saved is:

\[ \text{Quantity saved} = 8 \text{ quintals} - (10\% \text{ of } 8 \text{ quintals}) = 8 - 0.8 = 7.2 \text{ quintals} \]

**Hint:** To find the quantity after a percentage loss, subtract the lost quantity from the original quantity.

### Step 3: Calculate the Selling Price (SP) for a 15% profit
To earn a profit of 15%, we first need to find the desired selling price based on the cost price.

\[ \text{Desired Profit} = 15\% \text{ of Total Cost Price} = 0.15 \times 3600 = 540 \text{ Rs.} \]

Now, add this profit to the total cost price to find the total selling price:

\[ \text{Total Selling Price} = \text{Total Cost Price} + \text{Desired Profit} = 3600 + 540 = 4140 \text{ Rs.} \]

**Hint:** To calculate the selling price for a desired profit, add the profit amount to the total cost price.

### Step 4: Calculate the Selling Price per quintal
Now, we need to find the selling price per quintal based on the quantity saved (7.2 quintals):

\[ \text{Selling Price per quintal} = \frac{\text{Total Selling Price}}{\text{Quantity saved}} = \frac{4140}{7.2} \]

Calculating this gives:

\[ \text{Selling Price per quintal} = 575 \text{ Rs. per quintal} \]

**Hint:** To find the selling price per unit, divide the total selling price by the quantity available for sale.

### Final Answer
The rice trader should sell the rice at Rs. 575 per quintal to earn a 15% profit.

---