Books are bought at prices ranging from Rs. 200 to Rs. 350 and sold at prices ranging from Rs. 300 to Rs. 425. What is the greatest possible total profit that can be made by selling eight books?

Introduction / Context:
This question is about maximizing profit when both cost prices and selling prices vary within given ranges. It checks understanding of how to choose the most favourable combination of minimum costs and maximum selling prices to get the greatest possible profit when buying and selling multiple items.

Given Data / Assumptions:

• Cost prices of individual books lie between Rs. 200 and Rs. 350.
• Selling prices of individual books lie between Rs. 300 and Rs. 425.
• Exactly eight books are bought and sold.
• We are asked for the greatest possible total profit, assuming the trader can choose any allowed prices within the given ranges.

Concept / Approach:
Profit on each book is selling price minus cost price. To maximize total profit, each book should be bought as cheaply as possible and sold as expensively as possible, within the allowed ranges. Therefore, we use the lowest possible cost price and the highest possible selling price for every book and then multiply the resulting profit per book by the total number of books, which is eight.

Step-by-Step Solution:
Step 1: Minimum allowable cost price per book = Rs. 200.Step 2: Maximum allowable selling price per book = Rs. 425.Step 3: Maximum profit per book = 425 - 200 = Rs. 225.Step 4: Number of books sold = 8.Step 5: Maximum total profit = profit per book * number of books = 225 * 8 = Rs. 1800.

Verification / Alternative check:
Consider one book: if it is bought at Rs. 350 (the highest cost) and sold at Rs. 300 (the lowest selling price), there would be a loss.However, the problem asks for the greatest possible profit, so we always pair the minimum cost with the maximum selling price.Using Rs. 225 profit per book and eight books again leads to Rs. 1800, confirming the calculation.

Why Other Options Are Wrong:
Rs. 600 and Rs. 1200 assume lower per-book profits, which would come from less favourable price combinations. Rs. 1500 is still below the maximum possible Rs. 1800 and corresponds to a lower effective gain per book. The option “None of these” is incorrect because Rs. 1800 is achievable using the extreme points in the allowed ranges.

Common Pitfalls:
Students sometimes average the cost and selling price ranges and calculate profit based on average values, which does not give the maximum possible profit. Others mistakenly think that each book must be bought at different prices, whereas the question allows every book to be bought at the minimum and sold at the maximum price. For “greatest possible” style questions, always consider the extreme favourable values within the given constraints.

Final Answer:
The greatest possible total profit on eight books is Rs. 1800.