The average price of 10 books is Rs. 12. The average price of 8 of these books is Rs. 11.75. Of the remaining two books, the price of one book is 60% more than the price of the other. What is the price of each of these two books?

Introduction / Context:
This question combines average price calculations with percentage increase. It tests whether you can handle average to total conversions and then apply a percentage relationship between two unknown prices in order to determine their individual values from a known combined total.

Given Data / Assumptions:

• There are 10 books in total.

• Average price of all 10 books = Rs. 12.

• Average price of 8 books (a subset of these) = Rs. 11.75.

• The remaining 2 books have prices related by: price of one book is 60% more than the price of the other.

• We need the prices of the two remaining books.

Concept / Approach:
First, we convert each average into total price. From the overall average we find the total cost of 10 books. From the average of 8 books we find the total cost of those 8 books. The difference between these totals gives the combined cost of the remaining two books. Next, if the cheaper book costs x rupees, then the costlier book costs x + 0.6x = 1.6x. Their combined price is x + 1.6x = 2.6x, which we set equal to the known total for the two books. Solving this gives the individual prices.

Step-by-Step Solution:
Total price of 10 books = 10 * 12 = Rs. 120. Total price of 8 books = 8 * 11.75 = Rs. 94. Total price of the remaining two books = 120 − 94 = Rs. 26. Let the cheaper book cost = x rupees. Then the costlier book is 60% more, so its price = x + 0.6x = 1.6x. Combined price = x + 1.6x = 2.6x. Set 2.6x = 26, so x = 26 / 2.6 = 10. Therefore, cheaper book price = Rs. 10 and costlier book price = 1.6 * 10 = Rs. 16.

Verification / Alternative check:
Check by recomputing the totals: 8 books cost Rs. 94, the remaining two cost Rs. 10 and Rs. 16, so total = 94 + 10 + 16 = Rs. 120. Average price = 120 / 10 = Rs. 12, which matches the given overall average. Also, 16 is exactly 60% more than 10 since 10 * 0.6 = 6 and 10 + 6 = 16. Both conditions are satisfied, confirming the prices are correct.

Why Other Options Are Wrong:
Pairs such as 16 and 12 or 23 and 9 or 8 and 7 do not sum to Rs. 26, or do not maintain a 60% increase relationship between the two prices. For example, 16 and 12 sum to 28 and 16 is not 60% more than 12. Therefore, these options conflict with either the total price or the percentage condition. Only 10 and 16 fit both constraints.

Common Pitfalls:
A frequent mistake is to miscalculate the total for the 8 books or to forget to work with the combined price of two books. Another error is to misinterpret 60% more as 1.6 plus x instead of 1.6 times x. Always translate percentage increase as new price = original price * (1 + percentage in decimal). Using this correctly will prevent algebraic mistakes.

Final Answer:
The two remaining books are priced at Rs. 10 and Rs. 16 respectively.