A trader buys 500 kg of cotton for Rs. 9000. Due to rain, 10% of the cotton is spoiled and cannot be sold. At what selling price per kilogram should he sell the remaining cotton to earn a profit of 10% on his total investment?

Introduction / Context:
This question tests your ability to handle loss of quantity and desired profit simultaneously. The trader buys a bulk quantity of cotton, but a portion becomes unsaleable because it is spoiled by rain. He now needs to adjust the selling price of the remaining good cotton so that, despite the loss of quantity, he still earns a 10% profit on his total cost. This is a realistic business scenario and a classic concept in profit and loss involving wastage.

Given Data / Assumptions:
- Total quantity purchased = 500 kg of cotton. - Total cost price = Rs. 9000. - Percentage of cotton spoiled = 10%. - Spoiled cotton cannot be sold, so only the remaining 90% is saleable. - Desired overall profit on total cost = 10%. - We need the selling price per kg for the remaining cotton.

Concept / Approach:
First, calculate how many kilograms remain after 10% is spoiled. Then, compute the total revenue required to earn a 10% profit on the total cost price of Rs. 9000. Once you know the target revenue and the saleable quantity, the required selling price per kilogram is simply Target Revenue divided by Saleable Quantity. This method ensures that the loss from spoiled cotton is recovered in the price of the remaining cotton while still maintaining the desired profit percentage on the original investment.

Step-by-Step Solution:
Step 1: Find the quantity spoiled. Step 2: 10% of 500 kg = (10 / 100) * 500 = 50 kg. Step 3: Saleable quantity = 500 kg - 50 kg = 450 kg. Step 4: Total cost price (CP) = Rs. 9000. Step 5: Desired profit = 10% of CP = (10 / 100) * 9000 = Rs. 900. Step 6: Required total revenue (selling price of saleable cotton) = CP + Profit = 9000 + 900 = Rs. 9900. Step 7: Let required selling price per kg be SP. Step 8: Total revenue = SP * 450 = 9900. Step 9: Therefore SP = 9900 / 450 = Rs. 22 per kg.

Verification / Alternative check:
We can cross-check by recomputing the effective situation. If the trader sells 450 kg at Rs. 22 per kg, his revenue is 450 * 22 = Rs. 9900. His initial cost was Rs. 9000, so profit = 9900 - 9000 = Rs. 900. Profit percentage = (900 / 9000) * 100 = 10%. Thus all conditions of the question are satisfied exactly. The spoiled 50 kg are effectively absorbed in the higher price of the remaining 450 kg.

Why Other Options Are Wrong:
At Rs. 20 per kg or Rs. 25 per kg, the total revenue would be 450 * 20 = 9000 (no profit) or 450 * 25 = 11250 (much more than 10% profit). At Rs. 30 per kg, the profit would be even higher. Only Rs. 22 per kg gives exactly a 10% profit while accounting for the loss of 10% of the quantity. Therefore, all other options are inconsistent with the required profit percentage.

Common Pitfalls:
A common mistake is to calculate selling price per kg simply by adding 10% to the average cost per kg, without adjusting for the loss in quantity. The effective cost per kg of saleable cotton is higher than the original because some quantity has been lost. Another pitfall is to take 10% of 500 as extra profit instead of understanding that it represents wastage. Always adjust the saleable quantity first, then compute the required revenue for the target profit, and finally derive the selling price per kg.

Final Answer:
The trader should sell the remaining cotton at Rs. 22 per kg to earn a 10% profit on his total investment.