A rice trader buys 16 quintals of rice for Rs. 5632. 20% rice is lost in transportation. At what rate should he sell to earn 25% profit?

Options

A. Rs. 225.2 per quintal
B. Rs. 550 per quintal
C. Rs. 440 per quintal
D. Rs. 563.2 per quintal

Answer

To solve the problem step by step, we will follow the given details and calculations:

### Step 1: Calculate the Cost Price (CP) of Rice
The trader buys 16 quintals of rice for Rs. 5632.

**CP for 16 quintals = Rs. 5632**

### Step 2: Calculate the Loss in Rice Due to Transportation
The problem states that 20% of the rice is lost in transportation.

**Loss in rice = 20% of 16 quintals**
\[ \text{Loss} = \frac{20}{100} \times 16 = 3.2 \text{ quintals} \]

### Step 3: Calculate the Quantity of Rice Left After Loss
To find out how much rice is left after the loss, we subtract the loss from the initial quantity.

**Quantity left = 16 quintals - 3.2 quintals**
\[ \text{Quantity left} = 16 - 3.2 = 12.8 \text{ quintals} \]

### Step 4: Calculate the Selling Price (SP) for 25% Profit
To earn a profit of 25%, we need to calculate the Selling Price (SP) based on the Cost Price (CP).

**SP formula:**
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Here, the profit percentage is 25%.

**SP for 16 quintals:**
\[ \text{SP} = 5632 \times \left(1 + \frac{25}{100}\right) = 5632 \times 1.25 = 7040 \text{ Rs.} \]

### Step 5: Calculate the Selling Price per Quintal
Now, we need to find the selling price per quintal based on the quantity of rice left.

**SP per quintal:**
\[ \text{SP per quintal} = \frac{\text{Total SP}}{\text{Quantity left}} = \frac{7040}{12.8} \]

### Step 6: Perform the Calculation
Now we will perform the division to find the SP per quintal.

\[ \text{SP per quintal} = \frac{7040}{12.8} = 550 \text{ Rs.} \]

### Final Answer
The rate at which the trader should sell the rice to earn a 25% profit is **Rs. 550 per quintal**.

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