If the price of a book is reduced by ₹5, a buyer can purchase 2 more books for the same budget of ₹200. What was the original price per book?

Introduction / Context:This is a linear relation between price and quantity purchased under a fixed budget. When the unit price decreases, the number of items bought increases. The relationship can be modeled with a simple rational equation and solved algebraically.

Given Data / Assumptions:

• Budget = ₹200.
• Original price per book = p (₹).
• Reduced price per book = p − 5 (₹).
• At the reduced price, the buyer gets 2 more books than before.

Concept / Approach:Number of books originally = 200 / p. Number after reduction = 200 / (p − 5). The statement “2 more” translates to 200/(p − 5) = 200/p + 2. Solve this for p to find an admissible positive solution.

Step-by-Step Solution:

Verification / Alternative check:Original price ₹25 ⇒ can buy 200/25 = 8 books. Reduced price ₹20 ⇒ can buy 200/20 = 10 books. Increase = 2 as required.

Why Other Options Are Wrong:

• ₹30, ₹20, ₹15, ₹35: Substitution contradicts the “2 more books” condition for a ₹200 budget.

Common Pitfalls:

• Mistakes in setting up the equation (e.g., swapping p and p − 5 in denominators).
• Accepting a negative price solution from the quadratic (which is inadmissible).

Final Answer:₹ 25