A man buys 25 crates of oranges for a total of Rs 10,000. Unfortunately, 5 crates are completely spoiled and cannot be sold. To earn an overall profit of 25% on his total cost, at what price should he sell each of the remaining crates?

Introduction / Context:
This question combines the idea of total investment with losses due to spoilage and desired overall profit on the entire investment. The man buys a set of crates, loses some due to spoilage, and must adjust the selling price of the remaining crates to achieve a target profit percentage on the original cost. This is a standard type of problem in profit and loss related to damaged goods and effective pricing.

Given Data / Assumptions:

• Total crates bought = 25.
• Total cost = Rs 10,000.
• Number of crates spoiled and unsellable = 5.
• Number of crates remaining for sale = 25 - 5 = 20.
• Desired overall profit on total cost = 25%.
• We must find the selling price per remaining crate.

Concept / Approach:
First determine the total revenue required to achieve a 25% profit on the initial investment of Rs 10,000. That revenue must be obtained by selling the remaining 20 crates, since 5 crates are completely spoiled. Then divide the required total revenue by the number of sellable crates to get the selling price per crate. The key idea is that the entire cost, including the cost of spoiled crates, has to be recovered along with the target profit from the crates that are actually sold.

Step-by-Step Solution:
Step 1: Total cost price TCP = Rs 10,000.Step 2: Desired profit percentage = 25%.Step 3: Desired profit amount = 25% of 10,000 = 0.25 * 10,000 = Rs 2,500.Step 4: Required total revenue (total selling price) = TCP + profit = 10,000 + 2,500 = Rs 12,500.Step 5: Number of good crates available for sale = 20.Step 6: Selling price per crate needed = Total revenue / number of sellable crates = 12,500 / 20.Step 7: 12,500 / 20 = 625.Step 8: Therefore each of the remaining crates must be sold at Rs 625.

Verification / Alternative check:
We can check the overall profit if each of the 20 crates is sold at Rs 625. Total selling revenue = 20 * 625 = Rs 12,500. Subtracting the original cost of Rs 10,000, we get a profit of Rs 2,500. The profit percentage is 2,500 / 10,000 * 100 = 25%, which matches the desired overall profit. This verifies that the computed price per crate is correct.

Why Other Options Are Wrong:
Option A (Rs 650) would give total revenue of 20 * 650 = Rs 13,000, which corresponds to a profit of Rs 3,000 or 30%, higher than the required 25%. Option C (Rs 600) yields 20 * 600 = Rs 12,000, which is a 20% profit only. Option D (Rs 575) gives 11,500 total revenue, just 15% profit. Only option B, Rs 625 per crate, produces exactly a 25% profit on the total cost.

Common Pitfalls:
Students sometimes calculate profit only on the remaining crates and ignore the cost of spoiled crates, which underestimates the required selling price. Others divide the original cost by the remaining crates instead of calculating the revenue required for the desired profit. It is important to remember that spoilage still counts as part of the investment, and the target profit is based on the total initial cost, not only on the cost of the unsplit portion.

Final Answer:
He should sell each of the remaining crates at Rs 625 to earn a 25% overall profit.