A bookseller buys 500 textbooks for a total of Rs. 20,000. He wants to sell them at a profit in such a way that the total profit is equal to the cost price of 50 textbooks, effectively getting 50 books “free”. At what profit percentage on cost price should he sell the books?

Introduction / Context:
This question presents a real-life type situation where a bookseller wants to earn a profit equivalent to the cost price of a certain number of books, effectively making those books “free” through his profit. The total cost price and the desired profit amount are both given indirectly. Such problems test your ability to relate total cost, total profit, and number of units to determine the required profit percentage. Understanding that “getting 50 books free” means the profit should equal the cost of 50 books is the key conceptual step.

Given Data / Assumptions:
- Total number of textbooks bought = 500. - Total cost price of 500 textbooks = Rs. 20,000. - The bookseller wants total profit equal to the cost price of 50 textbooks. - We must find the required profit percentage on cost price.

Concept / Approach:
First, we compute the cost price per textbook. Then we find the cost price of 50 textbooks, which is the desired total profit. The profit percentage is simply (Desired Profit / Total Cost Price) * 100. Once the profit percentage is known, it tells us how much above cost price the selling price per book should be on average. There is no need to explicitly find the selling price per book, because the question only asks for the percentage profit.

Step-by-Step Solution:
Total cost price of 500 textbooks = Rs. 20,000. Cost price per textbook = 20,000 / 500. Compute: 20,000 / 500 = 40, so CP per textbook = Rs. 40. Cost price of 50 textbooks = 50 * 40 = Rs. 2,000. The bookseller wants his total profit to be Rs. 2,000. Total cost price of all books = Rs. 20,000. Profit percentage = (Total Profit / Total Cost Price) * 100. So, Profit% = (2,000 / 20,000) * 100. Compute: 2,000 / 20,000 = 1 / 10 = 0.10. Thus, Profit% = 0.10 * 100 = 10%.

Verification / Alternative check:
If profit is 10% on Rs. 20,000, profit amount = 0.10 * 20,000 = Rs. 2,000. We already saw that the cost price of 50 textbooks is Rs. 2,000. Therefore, with a 10% profit, he gains exactly the cost of 50 textbooks, matching his aim of “getting 50 books free”. This confirms that the required profit percentage is correctly computed as 10%.

Why Other Options Are Wrong:
- 20% profit would give Rs. 4,000 profit, which equals the cost price of 100 textbooks, not 50. - 15% profit yields Rs. 3,000, which corresponds to the cost of 75 textbooks. - 10.5% and 12% give profits slightly larger than Rs. 2,000, overshooting the target of 50 free books.

Common Pitfalls:
Some learners misinterpret “50 books free” and think he needs to sell 450 books at cost, rather than understanding that profit must equal the cost of 50 books. Another frequent error is to calculate profit percentage based on the value of 50 books instead of on the value of 500 books. Mixing up the roles of total cost and total profit in the percentage formula can also lead to incorrect answers.

Final Answer:
He should sell the books at an overall profit of 10% on cost price.