What's the best way to master Interchange with Unknown quickly?

Master Interchange with Unknown by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Interchange with Unknown

Interchange with Unknown problems involve two persons swapping positions, but one rank after swap is unknown. You must find the missing rank using the interchange relationship. These problems test your ability to work with incomplete swap information.

10Worksheets

200+Practice Questions

HardDifficulty

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 Interchange with Unknown

Prerequisites

Rank interchange concepts T = L + R - 1 formula Swap position dynamics Algebraic reasoning

Why This Matters: Interchange with Unknown problems appear in 1-2 questions in Banking PO and SSC CGL exams. They test reasoning with incomplete data.

How to Solve Interchange with Unknown Problems

Step 1: Identify known ranks before and after swap

Step 2: Use the fact that after swap, each person takes the other's position

Step 3: For a person, original rank from one end equals new rank of the other person from same end

Step 4: Use T = L + R - 1 to find missing ranks

Step 5: Solve for the unknown rank using the relationships

Step 6: Verify consistency of all ranks

Step 7: Present the answer

Pro Strategy: Use the fact that after swap, each person moves to the other's position. Convert all ranks to the same end for comparison. Use T = L + R - 1 to convert when needed.

Example Problem

Example: In a row of 50 persons, A and B swap positions. After swap, A is 30th from left. If B was originally 20th from right, what was A's original rank from left? Solution: Step 1: Total = 50, A's new left = 30, B's original right = 20 Step 2: After swap, A takes B's original position Step 3: So A's original left rank = B's original left rank Step 4: B's original left = Total - B's original right + 1 = 50 - 20 + 1 = 31 Step 5: Therefore A's original left = 31 Answer: 31

Pro Tips & Tricks

After swap, A's new left = B's original left
After swap, A's new right = B's original right
B's original left = T - B's original right + 1
The distance moved is the same for both persons

Shortcut Methods to Solve Faster

A_original_left = B_original_left = T - B_original_right + 1

If A_new_left given, A_original_left = B_original_left = T - B_original_right + 1

The swap preserves the sum of left and right ranks for each person

Common Mistakes to Avoid

Confusing whose original position goes to whom

Forgetting to convert right ranks to left before comparison

Assuming the swap affects ranks in both directions equally

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Interchange with Unknown. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.

Worksheet 1 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 2 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 3 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 4 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 5 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 6 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 7 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 8 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 9 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 10 Advanced Advanced level - Challenge yourself with complex problems