A librarian purchased 60 story books for his library at a certain average price per book. Later, he found that by spending Rs 336 more in total, he could have bought 4 extra books (making 64 books in all) and the overall average price per book would have been reduced by Re 1. What was the previous average price (in Rs) of each book?

Introduction / Context:
This question combines averages with a change in quantity and total cost. The librarian considers an alternative purchase plan in which he spends a bit more money, buys more books, and ends up with a lower average price. From these relationships, we can deduce the original average price per book.

Given Data / Assumptions:
• Number of books actually purchased = 60.• Original average price per book = x rupees (unknown).• So original total cost = 60x rupees.• If he spent Rs 336 more, total cost would be 60x + 336 rupees.• With this extra money, he could have bought 4 more books, that is 64 books.• In that case, the new average price per book would be (x - 1) rupees, that is Re 1 less.

Concept / Approach:
The key is to equate the total cost in the hypothetical case to the number of books multiplied by the new average price. This leads to a linear equation in x. Once we solve for x, we get the original average price per book. Such word problems are solved systematically by translating verbal relationships into algebraic equations.

Step-by-Step Solution:
Step 1: Let the original average price per book be x rupees.Step 2: Original total cost for 60 books = 60x.Step 3: In the hypothetical scenario, the librarian spends 336 rupees more, so new total cost = 60x + 336.Step 4: In that scenario, he could buy 64 books with average price (x - 1) rupees.Step 5: Therefore, new total cost can also be written as 64 * (x - 1).Step 6: Set the two expressions for new total cost equal: 60x + 336 = 64(x - 1).Step 7: Expand the right side: 64(x - 1) = 64x - 64.Step 8: So 60x + 336 = 64x - 64.Step 9: Rearrange to collect x terms: 336 + 64 = 64x - 60x.Step 10: 400 = 4x, so x = 400 / 4 = 100.

Verification / Alternative check:
With x = 100, original total cost is 60 * 100 = Rs 6000. If he spent 336 more, total becomes 6000 + 336 = Rs 6336. With 64 books, the new average price would be 6336 / 64 = 99 rupees, which is exactly Re 1 less than 100. This confirms that 100 rupees was the original average price per book.

Why Other Options Are Wrong:
Rs 84, Rs 83, Rs 68: If any of these were used as the original average, the equations would not balance. The total cost with 336 extra rupees would not equal the cost of 64 books at a reduced average price of x - 1.

Common Pitfalls:
Students sometimes confuse which average is larger or forget that the second average is lower by Re 1. Others may misinterpret the increase in number of books. Writing down the algebraic equation carefully and following the steps avoids such confusion.

Final Answer:
The previous average price of each book was Rs 100.