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Linear Arrangement with Distance

Linear Arrangement with Distance problems involve placing persons in a row with specific distance constraints (e.g., 'There are 3 persons between A and B', 'A is 5th from left and B is 3rd from right'). These problems require calculating total positions and using gap formulas.

10Worksheets
200+Practice Questions
HardDifficulty
3-4 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 Linear Arrangement with Distance

Linear Arrangement with Distance problems involve placing persons in a row with specific distance constraints (e.g., 'There are 3 persons between A and B', 'A is 5th from left and B is 3rd from right'). These problems require calculating total positions and using gap formulas.

Prerequisites

Linear arrangement basics Position arithmetic (from left/right) Gap calculation formulas Understanding of 'between' concept
Why This Matters: Linear Arrangement with Distance problems appear in 1-2 questions in SSC CGL and Banking exams. They test positional arithmetic and gap calculation.

How to Solve Linear Arrangement with Distance Problems

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Step 1: Identify the total number of positions (if given) or calculate from clues

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Step 2: Use formulas: Position from left + Position from right = Total + 1

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Step 3: For persons between A and B: |pos_A - pos_B| = number_between + 1

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Step 4: If positions are given from different ends, convert to same reference

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Step 5: Solve for unknown positions using equations

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Step 6: Draw the row with all persons placed

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Step 7: Answer the specific question

Pro Strategy: Always convert all positions to the same reference (e.g., all from left). Use the formula: Position from left = Total - Position from right + 1. Number between = |pos1 - pos2| - 1.

Example Problem

Example: In a row of 50 people, A is 15th from left. B is 20th from right. How many people are between A and B? Solution: Step 1: Total = 50, A_left = 15, B_right = 20 Step 2: B_left = Total - B_right + 1 = 50 - 20 + 1 = 31 Step 3: A is at 15, B at 31 Step 4: Persons between = |31 - 15| - 1 = 16 - 1 = 15 Answer: 15 people between A and B

Pro Tips & Tricks

  • Position from left + Position from right = Total + 1
  • Number of persons between A and B = |pos_A - pos_B| - 1
  • If A is to the left of B, then pos_A < pos_B
  • 'Exactly in the middle' means positions are equidistant from ends
  • For odd number between, the middle position is the average
  • If positions are unknown, use variables and solve equations

Shortcut Methods to Solve Faster

If A is mth from left and B is nth from right, B is (Total - n + 1)th from left
Persons between = Total - (m + n)
If A and B are at ends, persons between = Total - 2
Middle position = (Total + 1)/2 for odd total

Common Mistakes to Avoid

Forgetting to subtract 1 when counting persons between
Not converting positions to same reference before calculating
Assuming left and right positions are directly comparable
Miscalculating when A and B positions are reversed

Exam Importance

Linear Arrangement with Distance 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 Linear Arrangement with Distance?

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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