Nitin ranks 18th in a class of 49 students when counted from the top. What is his rank from the last in the same class?

Introduction / Context:
This is a simple ranking question where you must convert a position from the top into a position from the bottom. Questions like this appear frequently in competitive exams to ensure that you are comfortable with basic positional arithmetic in ordered lists such as classes or queues.

Given Data / Assumptions:

- There are 49 students in the class.- Nitin is 18th from the top.- We assume all positions are counted without gaps and that there are no ties.

Concept / Approach:
If we know a student's rank from the top and the total number of students, we can calculate the rank from the bottom using a simple formula: rank from bottom = total students - rank from top + 1. This formula works because the sum of the position from the top and the position from the bottom is always total + 1 for the same person.

Step-by-Step Solution:
Step 1: Total number of students N = 49.Step 2: Nitin's rank from the top is 18.Step 3: Use the formula: rank from bottom = N - rank from top + 1.Step 4: Substitute the values: rank from bottom = 49 - 18 + 1.Step 5: Compute 49 - 18 = 31.Step 6: Add 1 to get 31 + 1 = 32.Step 7: Therefore, Nitin is 32nd from the last.

Verification / Alternative check:
We can check the consistency of the formula: for any given person, rank from top + rank from bottom should equal total + 1. Here, 18 (from top) + 32 (from bottom) = 50, which equals 49 + 1. This confirms that the calculation is correct and no mistake has been made in applying the formula.

Why Other Options Are Wrong:
If we chose 31, the sum of ranks from top and bottom would be 18 + 31 = 49, which is not equal to total + 1. Option 18 wrongly suggests the same rank from top and bottom, which would only happen if Nitin were exactly in the middle of an odd number of students. Option 19 is also inconsistent with the required sum. Only 32 satisfies thecorrect positional relationship.

Common Pitfalls:
Some candidates wrongly subtract the rank directly from the total without adding 1, leading to an answer of 31. Others get confused between the ideas of top and bottom and may even try to average positions. Remembering the simple formula and its justification prevents such errors.

Final Answer:
Nitin's rank from the last is 32.