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Rank Interchange - Total

Rank Interchange problems involve two persons swapping positions in a row. After the swap, the rank of one person from one end is given. You must find the total number of persons or the new rank of the other person. These problems test your ability to track positional changes after swapping.

10Worksheets
200+Practice Questions
MediumDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Rank Interchange - Total

Rank Interchange problems involve two persons swapping positions in a row. After the swap, the rank of one person from one end is given. You must find the total number of persons or the new rank of the other person. These problems test your ability to track positional changes after swapping.

Prerequisites

Position from one side concepts Formula: T = L + R - 1 Understanding of interchange effects Basic algebra
Why This Matters: Rank Interchange problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of position swapping dynamics.

How to Solve Rank Interchange - Total Problems

1

Step 1: Identify the ranks of both persons before interchange (if given)

2

Step 2: Identify the new rank of one person after interchange

3

Step 3: Use the fact that after interchange, a person takes the other's position

4

Step 4: Total persons = New Left Rank of Person A + Original Right Rank of Person B - 1

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Step 5: Alternatively, T = Original Left Rank of Person B + New Right Rank of Person A - 1

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Step 6: Calculate the total or the unknown rank

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Step 7: Verify the result by checking consistency

Pro Strategy: After interchange, each person takes the other's position. Use T = New rank of A from one end + Original rank of B from the opposite end - 1 to find total.

Example Problem

Example: In a row, A is 12th from left and B is 18th from right. They interchange positions. Now A becomes 20th from left. Find total persons. Solution: Step 1: A's original left rank = 12, B's original right rank = 18 Step 2: After interchange, A's new left rank = 20 Step 3: Total persons = New left rank of A + Original right rank of B - 1 Step 4: = 20 + 18 - 1 = 37 Answer: 37 persons

Pro Tips & Tricks

  • T = New_L_A + Original_R_B - 1
  • T = Original_L_B + New_R_A - 1
  • The distance a person moves equals the difference in ranks
  • Both persons move the same number of positions in opposite directions
  • After swap, the sum of a person's left and right ranks remains T + 1

Shortcut Methods to Solve Faster

Total = New left rank of swapper + Original right rank of swapped - 1
The person who moves left increases left rank, decreases right rank
Original and new ranks of the same person sum to 2T + 2? Check carefully

Common Mistakes to Avoid

Using original ranks of the same person instead of the other person
Forgetting to subtract 1 in the formula
Confusing which person's new rank to use

Exam Importance

Rank Interchange - Total is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Rank Interchange - Total?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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