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:
This question combines average calculation with percentage increase. You know the overall average price of 10 books, the average price of 8 of them, and that one of the remaining two books is 60% more expensive than the other. You must find the individual prices of the two remaining books.

Given Data / Assumptions:
Average price of 10 books = Rs 12. Average price of 8 of these books = Rs 11.75. Of the remaining two books, the price of one is 60% more than the price of the other. We need to find the prices of these two books.

Concept / Approach:
First, convert averages to totals: Total price of 10 books = 10 * 12. Total price of 8 books = 8 * 11.75. The sum of the prices of the remaining two books is the difference between these totals. Then use the condition that one price is 60% more than the other to set up a simple equation.

Step-by-Step Solution:
Step 1: Total price of all 10 books. Total = 10 * 12 = Rs 120. Step 2: Total price of 8 books. Total of 8 books = 8 * 11.75 = Rs 94. Step 3: Sum of prices of the remaining two books. Sum of two books = 120 - 94 = Rs 26. Step 4: Let the cheaper of the two books cost x rupees. Then the costlier book is 60% more than x, so its price = x + 0.60x = 1.6x. Step 5: Use the sum condition. x + 1.6x = 26. 2.6x = 26. x = 26 / 2.6 = 10. So the cheaper book costs Rs 10 and the costlier book costs 1.6 * 10 = Rs 16.

Verification / Alternative Check:
Check: The two prices are Rs 10 and Rs 16, sum is Rs 26, and 16 is indeed 60% more than 10. Also, total of all 10 books is 94 + 26 = 120, giving average 120 / 10 = 12, which matches the given data.

Why Other Options Are Wrong:
Rs 16 and Rs 12: Sum is Rs 28 and 16 is not 60% more than 12. Rs 23 and Rs 9: Sum is Rs 32, which does not match Rs 26. Rs 8 and Rs 7: Sum is Rs 15, far from Rs 26, and there is no 60% relation. Rs 9 and Rs 14.40: Sum is Rs 23.40, and again does not match the required total of Rs 26.

Common Pitfalls:
Some students mistakenly treat 60% more as 60% of the combined total instead of 60% of the smaller price. Others forget to first compute the sum of the two unknown prices from the average information. Always find the total, then use the percentage relation correctly.

Final Answer:
The prices of the two remaining books are Rs 10 and Rs 16.