In a row of books, a book of English is 16th from the left end. A book of Mathematics is 12th from the right end. The Mathematics book is 6th to the right of the English book. How many books are there in the row in total?

Introduction / Context:
This is another rank and position problem with two specific books in a row. You are given each book’s position from one end and the relative separation between them. Using this information, you must find the total number of books in the row. These questions practice moving between left side positions, right side positions and total counts using standard relationships.

Given Data / Assumptions:

• The English book is 16th from the left end of the row.
• The Mathematics book is 12th from the right end of the row.
• The Mathematics book is 6th to the right of the English book.
• All books are arranged in a straight row with no gaps in between.

Concept / Approach:
First, use the relative information that the Mathematics book is 6th to the right of the English book to determine its position from the left. Then, use the relation between left and right positions for a known total N: if an item is at position L from the left and R from the right, then the total number of items is N = L + R - 1. Substituting the known left and right positions of the Mathematics book into this formula gives the total number of books.

Step-by-Step Solution:
Let the position of the English book from the left be E = 16. The Mathematics book is 6th to the right of the English book. So its position from the left, call it M, is M = 16 + 6 = 22. We are told that the Mathematics book is also 12th from the right end. Let the total number of books be N. For the Mathematics book, we then have left position L = 22 and right position R = 12. Use the formula N = L + R - 1. Substitute L = 22 and R = 12 to get N = 22 + 12 - 1. Compute: 22 + 12 = 34, and 34 - 1 = 33. Therefore, there are 33 books in the row.

Verification / Alternative check:
Check consistency by recomputing positions. If N = 33, a book at position 22 from the left has position from the right equal to 33 - 22 + 1 = 12, which matches the given position of the Mathematics book from the right. Also, the English book at position 16 and the Mathematics book at 22 are separated by 6 positions when counting to the right, since 22 - 16 = 6. This confirms that N = 33 satisfies all given conditions.

Why Other Options Are Wrong:
If N were 32 or 34, a book at position 22 from the left would not be 12th from the right. For N = 32, the right position would be 32 - 22 + 1 = 11. For N = 34, it would be 34 - 22 + 1 = 13. Similar contradictions arise for 31 or 30. Only N = 33 maintains both the 22nd position from the left and the 12th from the right for the Mathematics book while preserving the separation of 6 positions to the right of the English book.

Common Pitfalls:
A common error is to misinterpret “6th to the right” and use 5 instead of 6 when adding, or to forget the -1 term in the formula N = L + R - 1. Some candidates also confuse the positions of the two books and mistakenly use the English book’s right position, which is not given. Working step by step, and clearly labeling positions, helps avoid these mistakes.

Final Answer:
The total number of books in the row is 33.