A trader buys 800 kilograms of tomatoes for a total cost of Rs 7200.\nDuring transportation 10% of the tomatoes are damaged and cannot be sold.\nAt what selling price per kilogram should the trader sell the remaining tomatoes to earn a profit of 30% on his total cost?

Introduction / Context:
This problem combines the ideas of percentage loss of quantity with required selling price to achieve a target profit. The trader buys a certain mass of tomatoes, but a percentage of them are spoiled in transit, leaving fewer kilograms available for sale. Even though some tomatoes are wasted, the trader still wants to achieve a planned profit on the original investment. This type of question is very common in profit and loss sections of aptitude exams and reflects how wastage affects pricing decisions in real business situations.

Given Data / Assumptions:

• Total quantity purchased = 800 kilograms of tomatoes.
• Total cost price for 800 kilograms = Rs 7200.
• Percentage of tomatoes damaged = 10% of the total quantity.
• Target profit on total cost = 30%.
• Damaged tomatoes cannot be sold and generate no revenue.
• We need the selling price per kilogram of the remaining good tomatoes.

Concept / Approach:
First, calculate the trader total cost price. Then compute the selling price needed to secure a 30% profit on that cost. Next, determine the quantity of tomatoes that remain after 10% are damaged. Finally, divide the required total selling price by the number of kilograms available for sale to obtain the selling price per kilogram. The key idea is that profit is based on the original cost, not on the cost of only the undamaged quantity, so wastage forces a higher per kilogram selling price.

Step-by-Step Solution:
Step 1: Total cost price (CP) for 800 kg = Rs 7200. Step 2: Required profit = 30% of CP = 30 / 100 * 7200 = 0.3 * 7200 = Rs 2160. Step 3: Required total selling price (SP total) = CP + profit = 7200 + 2160 = Rs 9360. Step 4: Tomatoes damaged = 10% of 800 kg = 10 / 100 * 800 = 80 kg. Step 5: Good tomatoes available for sale = 800 kg - 80 kg = 720 kg. Step 6: Selling price per kg = SP total / good quantity = 9360 / 720. Step 7: Compute 9360 / 720 = 13. Step 8: Therefore the trader should sell the remaining tomatoes at Rs 13 per kilogram.

Verification / Alternative check:
As a check, multiply the selling price per kilogram by the saleable quantity. At Rs 13 per kilogram for 720 kilograms, total revenue is 13 * 720 = Rs 9360. Subtracting the original cost of Rs 7200 from this revenue gives a profit of Rs 2160. The profit percentage is 2160 / 7200 * 100 = 30%, which matches the required profit rate. This confirms that Rs 13 per kilogram is the correct selling price under the given conditions of wastage and profit requirement.

Why Other Options Are Wrong:
If the price were Rs 9 per kilogram, revenue would be 9 * 720 = Rs 6480, which is less than the cost and leads to a loss. At Rs 10 per kilogram, revenue would be 7200, meaning zero profit. At Rs 12 per kilogram, revenue would be 8640, giving a profit of only 1440, which is 20% of 7200, not 30%. Therefore only Rs 13 per kilogram gives the exact 30% profit, so the other options do not satisfy the problem requirement.

Common Pitfalls:
A typical error is to compute the selling price per kilogram based on the original total quantity of 800 kilograms instead of the reduced 720 kilograms. Another mistake is to treat the 10% damaged quantity as a price discount rather than loss of goods. Candidates also sometimes calculate profit percentage on the selling price rather than on the cost price. Careful attention to definitions of cost price, selling price, and profit, along with the effect of wastage on available quantity, helps avoid these issues.

Final Answer:
The trader must sell the good tomatoes at Rs 13 per kilogram to earn a 30% profit.