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Rank after Removal

Introduction

Questions on rank-after-removal ask how a person's position changes when some members are removed from the line/class. These appear frequently in aptitude tests because they test careful counting - identifying who was removed (above or below) is the key.

Mastering this pattern lets you quickly update ranks when people leave or when additional members are inserted.

Pattern: Rank after Removal

Pattern

Key idea: Only removals of people ahead of the person change their rank - new_rank = old_rank - (number of removed people who were ahead).

Variants you must recognise:

  • If x people who were ahead leave → new rank = old rank - x.
  • If x people behind leave → rank remains the same.
  • If removals are mixed (some ahead, some behind) → subtract only those who were ahead.
  • If asked for new total strength, update total = old total - total removed.

Step-by-Step Example

Question

There are 40 students in a class. Ravi is 10th from the top. Five students who were ahead of him leave the class. What is Ravi’s new rank from the top?

Solution

  1. Step 1: Identify original data

    Total = 40; Ravi’s old rank from top = 10 → so 9 students were ahead of him.

  2. Step 2: Count how many ahead have left

    Given: 5 students who were ahead of Ravi leave.

  3. Step 3: Apply the rule

    New rank = Old rank - (number of removed people who were ahead) = 10 - 5 = 5.

  4. Final Answer:

    Ravi’s new rank is 5th from the top.

  5. Quick Check:

    Originally 9 ahead → after 5 of those leave, 4 remain ahead → Ravi becomes 4 + 1 = 5th ✅

Quick Variations

1. If students behind leave → rank unchanged (only total reduces).

2. If you are given removals but not whether they were ahead/behind, determine positions (e.g., list positions) or ask for conversion to check which side they were.

3. When multiple people leave including some ahead and some behind → subtract only the count of those ahead.

4. If asked the new rank from the bottom, convert: New position from bottom = New total - New rank from top + 1.

Trick to Always Use

  • Step 1 → Convert the given rank to “people ahead” (people_ahead = rank - 1).
  • Step 2 → Subtract the number of removed people who were ahead: new_people_ahead = people_ahead - removed_ahead.
  • Step 3 → Convert back to rank: new_rank = new_people_ahead + 1.

Summary

Summary

  • When people ahead leave, reduce the person's rank by the number of those removed.
  • Removals behind the person do not change their rank (only the total decreases).
  • For mixed removals, count only those who were ahead and subtract them from the old rank.
  • To find new rank from bottom, update total first then convert: new_bottom = new_total - new_top + 1.

Example to remember:
If someone is 12th and 3 people ahead leave, new rank = 12 - 3 = 9th.

Practice

(1/5)
1. In a class of 50 students, Anu is ranked 12th from the top. If 4 students ahead of her leave the class, what will be her new rank?
easy
A. 8th
B. 9th
C. 10th
D. 11th

Solution

  1. Step 1: Original rank

    Anu’s old rank = 12 → 11 students were ahead.

  2. Step 2: Removals ahead

    4 students ahead leave.

  3. Step 3: New rank

    New rank = 12 - 4 = 8th.

  4. Final Answer:

    8th → Option A

  5. Quick Check:

    Originally 11 ahead, now 7 ahead → 7 + 1 = 8 ✅
Hint: Subtract number of people ahead who leave from old rank.
Common Mistakes: Subtracting all removals instead of only those ahead.
2. In a competition of 40 participants, Rohan ranks 7th from the top. If 3 participants who were ahead of him are disqualified, what is his new rank?
easy
A. 3rd
B. 4th
C. 5th
D. 6th

Solution

  1. Step 1: Given

    Old rank = 7; 3 participants ahead leave.

  2. Step 2: Compute

    New rank = 7 - 3 = 4th.

  3. Final Answer:

    4th → Option B

  4. Quick Check:

    Before: 6 ahead → now 3 ahead → rank = 4 ✅
Hint: Remove count only for those before the given rank.
Common Mistakes: Subtracting from total participants instead of from rank.
3. In a class of 60 students, Priya is ranked 15th from the top. If 5 students behind her leave the class, what will be her new rank?
easy
A. 16th
B. 14th
C. 15th
D. 13th

Solution

  1. Step 1: Observation

    Students behind do not affect rank from top.

  2. Step 2: Result

    Her position from top remains the same = 15th.

  3. Final Answer:

    15th → Option C

  4. Quick Check:

    No change since all 5 were behind ✅
Hint: If only those behind leave, rank remains unchanged.
Common Mistakes: Incorrectly reducing rank when removals are behind.
4. In a test of 45 students, Amit is 9th from the top. If 2 students ahead and 3 behind him leave, what is his new rank?
medium
A. 5th
B. 6th
C. 8th
D. 7th

Solution

  1. Step 1: Identify relevant removals

    Only 2 ahead affect the rank.

  2. Step 2: Compute

    New rank = 9 - 2 = 7th.

  3. Final Answer:

    7th → Option D

  4. Quick Check:

    2 ahead left → Amit moves up by 2 positions ✅
Hint: Ignore removals behind - only those ahead matter.
Common Mistakes: Subtracting all removals instead of only ahead ones.
5. In a group of 30 people, Kavya ranks 8th from the top. If 4 people ahead of her and 2 behind her leave, what is her new rank?
medium
A. 4th
B. 3rd
C. 5th
D. 6th

Solution

  1. Step 1: Count only those ahead

    4 ahead leave → affects rank.

  2. Step 2: Compute

    New rank = 8 - 4 = 4th.

  3. Final Answer:

    4th → Option A

  4. Quick Check:

    4 ahead gone → Kavya moves from 8 → 4 ✅
Hint: Subtract only people ahead who left the line.
Common Mistakes: Reducing total and using that incorrectly to get rank.

Mock Test

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