A librarian purchased 60 story books for a library at an average price of Rs x per book. Later he found that by spending Rs 336 more he could have obtained 4 extra books (a total of 64 books) and in that case the overall average price per book would have been reduced by Re 1. What was the original average price of each book in rupees?

Introduction / Context:
This problem is a classic example of using averages in a cost and quantity setting. A librarian buys a certain number of books at an unknown average price. Then he considers a different purchase plan with slightly more books and a slightly larger total cost, which changes the average price. Using this information, we can set up an equation and solve for the original average price per book.

Given Data / Assumptions:
- Number of books originally purchased = 60.
- Original average price per book = Rs x (unknown).
- Therefore original total cost = 60x rupees.
- New scenario: he spends Rs 336 more, so new total cost = 60x + 336 rupees.
- With this new total, he can buy 64 books instead of 60.
- In the new scenario, the average price per book is Re 1 less, that is x - 1 rupees per book.
- We must find the original average price x in rupees.

Concept / Approach:
The new total cost divided by the new number of books must equal the new average price. This gives an equation involving x. By simplifying and solving that equation, we obtain the original average price. The key is to express everything in terms of x and equate the two expressions for the new average price.

Step-by-Step Solution:
Step 1: Original total cost = 60x rupees.Step 2: New total cost after spending extra Rs 336 = 60x + 336 rupees.Step 3: In the new scenario, number of books = 64 and new average price = x - 1 rupees.Step 4: New average price is also equal to (60x + 336) / 64.Step 5: Set up the equation: (60x + 336) / 64 = x - 1.Step 6: Multiply both sides by 64: 60x + 336 = 64(x - 1).Step 7: Expand the right side: 60x + 336 = 64x - 64.Step 8: Rearrange: 336 + 64 = 64x - 60x.Step 9: This gives 400 = 4x, so x = 100.Step 10: Therefore, the original average price per book is Rs 100.

Verification / Alternative check:
With x = 100, original total cost is 60 * 100 = Rs 6000. New total cost is 6000 + 336 = Rs 6336. The librarian could buy 64 books, so new average price = 6336 / 64 = 99 rupees, which is indeed Re 1 less than the original average of Rs 100. This confirms that the result is correct.

Why Other Options Are Wrong:
If the average price were Rs 84 or Rs 83, the recalculated new average after adding Rs 336 and four books would not be exactly Re 1 lower. Rs 68 is far too low to produce the given relationship between costs and averages. Only Rs 100 satisfies the equation and the description given in the problem statement.

Common Pitfalls:
Common mistakes include forgetting that the new total cost is 60x plus 336, not 64x plus 336, or not applying the condition that the new average is exactly one rupee less. Some learners also confuse the number of books in the two scenarios. Always identify the original and new totals, quantities and averages clearly before writing the equation.

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