A trader buys 500 kg of cotton for Rs 9000. Due to rain, 10% of the cotton is spoiled and becomes unsaleable. At what rate per kg should he sell the remaining cotton in order to earn an overall profit of 10%?

Introduction / Context:
This question combines loss of quantity due to spoilage with the requirement of a target profit on the original investment. It shows a realistic business situation in which not all purchased goods can be sold. You must adjust the selling price of the remaining good quality cotton so that, despite the loss of some stock, the trader still earns a desired profit percentage overall.

Given Data / Assumptions:

• Total quantity of cotton bought = 500 kg.
• Total cost = Rs 9000.
• 10% of the cotton is spoiled and cannot be sold.
• The trader wants an overall profit of 10% on his investment.
• We assume spoiled cotton has no resale value.

Concept / Approach:
First, we find how many kilograms of cotton remain saleable after spoilage. Then we calculate the total revenue required to get a 10% profit on the total cost. Finally, the required selling price per kg is that revenue divided by the saleable quantity. This is a standard approach: Desired Revenue = Cost * (1 + profit_percent / 100).

Step-by-Step Solution:
Total quantity purchased = 500 kg.Total cost price = Rs 9000.Spoiled cotton = 10% of 500 kg = 0.10 * 500 = 50 kg.Saleable cotton = 500 kg - 50 kg = 450 kg.Trader wants 10% profit, so required total revenue = 9000 * (1 + 10 / 100) = 9000 * 1.10 = Rs 9900.Required selling price per kg = 9900 / 450.9900 / 450 = Rs 22 per kg.

Verification / Alternative check:
If he sells 450 kg at Rs 22 per kg, revenue = 450 * 22 = Rs 9900. Initial cost was Rs 9000, so profit = 9900 - 9000 = Rs 900. Profit percentage = 900 / 9000 * 100 = 10%. This confirms that selling at Rs 22 per kg achieves the desired overall gain despite 10% spoilage.

Why Other Options Are Wrong:
If he sells at Rs 20 per kg, revenue is 450 * 20 = Rs 9000, which gives no profit. At Rs 25 or Rs 30 per kg, profits would be much higher than 10%. For instance, at Rs 25, revenue is Rs 11250, giving 25% profit. Thus only Rs 22 per kg gives exactly a 10% profit on the total investment.

Common Pitfalls:
Some learners mistakenly try to apply the profit percentage only to the uns spoiled quantity or misinterpret the base for the profit calculation. Profit is always calculated on the original cost, not on the value of the remaining quantity. Another error is forgetting that the spoiled portion contributes zero revenue, which must be considered implicitly in the rate adjustment for the uns spoiled portion.

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