Calculating Selling Price for Grain Trader Profit

This problem involves a trader buying grain, incurring a loss during transportation, and then selling the remaining quantity to achieve a specific profit percentage. We need to determine the selling rate per kilogram for the remaining grain.

Step-by-Step Solution Analysis

Here's how we can solve this problem:

1. Understand the Initial Investment and Quantity

• The trader bought 200 kg of grain.
• The total cost price (CP) of the grain is \(\text{Rs. } 8,000\).

2. Calculate the Quantity of Grain Lost

• A loss of 4% of the grain occurred during transportation.
• Quantity lost = 4% of 200 kg
• Quantity lost \(= \frac{4}{100} \times 200 \text{ kg}\)
• Quantity lost \(= 4 \times 2 \text{ kg}\)
• Quantity lost \(= 8 \text{ kg}\)

3. Determine the Remaining Quantity of Grain

• The amount of grain left to sell is the initial quantity minus the quantity lost.
• Remaining grain \(= 200 \text{ kg} - 8 \text{ kg}\)
• Remaining grain \(= 192 \text{ kg}\)

4. Calculate the Target Total Selling Price

• The trader wants to earn a 20% profit on the total cost price (\(\text{Rs. } 8,000\)).
• Target profit amount = 20% of \(\text{Rs. } 8,000\)
• Target profit amount \(= \frac{20}{100} \times 8000 \text{ Rs.}\)
• Target profit amount \(= 20 \times 80 \text{ Rs.}\)
• Target profit amount \(= 1600 \text{ Rs.}\)
• The total selling price (SP) needed to achieve this profit is the cost price plus the target profit.
• Target Total SP = Cost Price + Target Profit
• Target Total SP \(= \text{Rs. } 8000 + \text{Rs. } 1600\)
• Target Total SP \(= \text{Rs. } 9600\)

5. Calculate the Selling Price Per Kilogram

• The trader must sell the remaining 192 kg of grain for a total of \(\text{Rs. } 9600\).
• Selling Price per kg = \(\frac{\text{Target Total SP}}{\text{Remaining Grain Quantity}}\)
• Selling Price per kg \(= \frac{\text{Rs. } 9600}{192 \text{ kg}}\)
• Selling Price per kg \(= \text{Rs. } 50 / \text{kg}\)

Summary of Calculations

Based on these calculations, the trader should sell the rest of the grain at a rate of Rs. 50 per kg to earn a 20% profit on the initial cost price.

Revision Table: Key Concepts in Profit and Loss

Additional Information: Handling Percentage Loss in Quantity

In problems involving loss in quantity, like the grain lost in transportation, it's crucial to first calculate the actual quantity lost and then find the remaining quantity. The profit calculation is then based on the initial cost price but must be achieved by selling only the remaining quantity. The selling price per unit is therefore calculated by dividing the target total selling price by the quantity available for sale.

This method ensures that the profit is correctly accounted for based on the initial investment, even when the sellable quantity is reduced due to losses.