Linear Arrangement Reasoning for Bank Exams 2026: Basics, Tricks & Examples

Linear Arrangement is a fundamental topic in reasoning ability for competitive exams, especially bank exams. These puzzles require candidates to arrange people or objects in a straight line or multiple parallel lines according to specific conditions. 

Mastering Linear Arrangement Reasoning for Bank Exams 2026 is crucial as it tests logical deduction and systematic problem-solving skills, forming a significant part of the reasoning section. 

Types of Linear Arrangement Questions

Linear Arrangement questions in banking exams primarily fall into four categories:

1. Single Row, All Facing North: All individuals are in one line, facing the same direction (North).

2. Single Row, Mixed Directions: Individuals are in one line, with some facing North and others facing South.

3. Parallel Rows: Two rows of individuals face each other.

4. Uncertain Number of Persons: The total number of individuals in the line is not given and must be determined.

This blog focuses on the first three types.

Basic Concepts of Linear Arrangement (North-Facing)

When all individuals in a line are facing North:

• The direction to their right is the Right Side.

• The direction to their left is the Left Side.

Key Distinctions in Terminology:

• Specific vs. General Position:

• "B is third to the right of A": This indicates a specific position. From A's position, count three places to the right to place B.

• "C is to the left of B": This is a general position. The exact spot is not specified. C could be anywhere to B's left, unless more information is provided.

• Handling Ambiguity: When a person's exact position is unknown, test all possible places that fit the conditions. For instance, if "E is third to the left of D" and D's position is not fixed, check each potential spot for D to satisfy the condition.

Worked Example 1: Single Row, North-Facing

Problem: Eight people (A, B, C, D, P, Q, R, S) are sitting in a single row, all facing North.

• Only 3 people sit between P and C.

• 2 people sit between C and S.

• S sits at one of the extreme ends.

• B is to the immediate left of C.

• Only 1 person sits between B and R.

• R is not a neighbor of P.

• The number of people to the right of R is equal to the number of people to the left of D.

• P is not a neighbor of Q.

Solution Process:

1. Anchor with Ambiguity: Start with "S sits at one of the extreme ends," creating two initial cases.

2. Sequential Deductions: Use "2 people sit between C and S" and "3 people sit between P and C" to place C and P relative to S. Then, place B based on "B is to the immediate left of C."

3. Case Elimination: Employ "1 person sits between B and R" and "R is not a neighbor of P" to narrow R's position. A critical condition, "The number of people to the right of R is equal to the number of people to the left of D," will then help eliminate one case as it cannot be satisfied.

4. Finalizing Arrangement: In the remaining valid case, use "P is not a neighbor of Q" to place Q, and then the last person (A) in the remaining slot. The strategy involves using definite conditions to build possibilities and then eliminating them with further constraints.

Worked Example 2: Single Row, 10 People, North-Facing

Problem: Ten people are in a row facing North.

• S is to the right of K and to the left of P.

• 4 people sit between O and M.

• Q is second to the right of W.

• 5 people sit to the right of G.

• 1 person sits between M and U. U is a neighbor of Z.

• 3 people sit between W and O.

• 2 people sit between G and W.

Solution Process:

1. Anchor Condition: Begin with "5 people sit to the right of G," which fixes G's position in the 10-person row.

2. Case Generation: Use "2 people sit between G and W" to create two cases for W (left or right of G).

3. Sequential Placements & Elimination: In each case, place Q ("Q is second to the right of W"), then O ("3 people sit between W and O"), and M ("4 people sit between O and M"). Apply "1 person sits between M and U" and "U is a neighbor of Z." One case will be eliminated as it fails to accommodate Z next to U.

4. Final Positions: In the remaining case, place K, S, and P based on "S is to the right of K and to the left of P" (K-S-P order) in the remaining consecutive seats.

Worked Example 3: Single Row, 9 People, North-Facing

Problem: Nine people are in a row facing North.

• J sits fourth from the right end.

• 3 people sit between J and K.

• K is to the immediate right of D.

• 1 person sits between K and H.

• 2 people sit between B and H.

• J is to the immediate right of F.

• N is to the immediate left of P.

• 2 people sit between J and P.

Solution Process:

1. Anchor Position: Start with "J sits fourth from the right end," fixing J's position.

2. Building Sequentially: Place K using "3 people sit between J and K." Then place D using "K is to the immediate right of D." Follow this to place H ("1 person sits between K and H") and B ("2 people sit between B and H").

3. Resolving Ambiguity: Address "2 people sit between J and P" by considering possibilities for P (left or right of J). Test these with "N is to the immediate left of P." One possibility for P will be invalid as it prevents N's placement, thereby fixing P and N.

4. Completing the Arrangement: Place F using "J is to the immediate right of F." The last person (E) fills the final empty seat.

Concepts for Mixed-Direction Arrangements (North/South)

When people in a row face different directions (North and South), the concept of left and right becomes relative to the direction each person is facing.

• For a North-facing person: Right is towards their east, Left is towards their west.

• For a South-facing person: Right is towards their west, Left is towards their east.

The Golden Rule: You cannot determine the left or right of a person without knowing their facing direction. If the direction is unknown, you must consider both possibilities: Assume North-facing and apply the condition, then assume South-facing and apply the condition. This often requires managing parallel cases until other conditions resolve the ambiguity.

Worked Example 4: Single Row, North/South Facing

Problem: Eight people (P, Q, R, S, T, U, V, W) are in a row with some facing North and some South.

• V is third from one of the ends.

• S is second to the right of V. V is 5 places away from R (i.e., 4 people between them).

• R is to the left of V.

• W and V are immediate right of each other (implying they face opposite directions and are neighbors).

• P is to the immediate left of R.

• Two adjacent people do not face the same direction.

• At least two people sit between W and U. U faces North.

• Q is equidistant from S and P.

Solution Process:

1. Anchor & Structure: The conditions "V is third from an end," "S is second to the right of V," and "R is to the left of V with 4 people between them" define a fixed relative structure (R _ _ _ _ V _ S) for all 8 positions.

2. Case for Direction: Create cases based on V's facing direction (North or South) to place S accordingly.

3. Powerful Constraint: Apply "Two adjacent people do not face the same direction." This rule dictates alternating directions (N-S-N-S…). Use it with "W and V are immediate right of each other" to place W and determine its direction.

4. Case Elimination: Use "P is to the immediate left of R" to place P. One of the initial cases for V's direction will violate the alternating direction rule, leading to its elimination.

5. Final Deductions: In the valid case, place U based on "U faces North" and "at least two people between W and U." Place Q based on "Q is equidistant from S and P." The last person (T) fills the remaining spot.

Worked Example 5: Single Row, 9 People, North/South Facing

Problem: Nine people (P-W and X) in a row.

• Consecutive alphabetically named persons are not neighbors.

• Two adjacent persons do not face the same direction.

• X faces North and an equal number of persons sit on both sides of X.

• W is to the left of X and is second from one of the ends.

• S is to the immediate right of W.

• T is third to the right of V. T is not at an end.

• R is not a neighbor of U.

• At least two people sit between R and P. P is not at an end.

Solution Process:

1. Anchor Position: "X faces North and an equal number of persons sit on both sides of X" places X in the exact middle (5th position) of the 9-person row.

2. Establishing Directions: "Two adjacent persons do not face the same direction" combined with X facing North, fixes the alternating directions for the entire row (S-N-S-N-S-N-S-N-S).

3. Sequential Placement: Use "W is to the left of X and is second from one of the ends" to place W. Then, "S is to the immediate right of W" allows placement of S (W's direction is known from the alternating pattern).

4. Handling Complex Logic: For "T is third to the right of V" and "T is not at an end," coupled with the "consecutive alphabetically named persons are not neighbors" rule, systematically test possible positions for V. This will lead to the elimination of invalid placements until V and T are uniquely fixed.

5. Finalizing with Constraints: Place P, Q, R, and U using the remaining conditions, particularly "R is not a neighbor of U" and "At least two people sit between R and P," and the alphabetic neighbor rule. This leads to the final arrangement.

Introduction & Example 6: Parallel Row Arrangement

Parallel row arrangements involve two rows of people facing each other. Typically, one row faces North and the other faces South. This means individuals in opposite rows face each other.

Problem: Ten people in two parallel rows of five.

• Row 1 (South-facing): A, B, C, D, E

• Row 2 (North-facing): P, Q, R, S, T

• D is third to the right of C.

• C faces S.

• P is second to the right of T.

• P faces either B or E.

• B is to the immediate left of E.

• Q is third to the left of R.

Solution Process:

1. Anchor & Case Creation: Start with a strong condition in one row, like "D is third to the right of C" in the South-facing row. This creates two possible arrangements for that row, based on where C is placed.

2. Connecting Rows: Use the facing condition, "C faces S," to place S in the opposite row for both cases.

3. Eliminating Cases: Employ a condition that strongly constrains positions, such as "B is to the immediate left of E." In one of the initial cases, this block (E-B) will not fit, leading to its elimination.

4. Final Deductions: In the valid case, use "P faces either B or E" and "P is second to the right of T" to place P and T in Row 2. One sub-possibility for P will be invalid. Finally, place Q and R using "Q is third to the left of R" and the last person (A) in the remaining spot.

Strategy for Improving Puzzle-Solving Skills

If you struggle with puzzles, adopt a systematic approach:

1. Analyze Your Mistakes: Identify the exact reason for getting stuck. This reveals conceptual gaps.

2. Follow a Step-by-Step Progression: Avoid jumping to complex puzzles. Start with Clerk Pre-level, progress to PO Pre-level, and only then attempt more challenging Mains-level puzzles. This builds confidence and foundational understanding.

3. Practice Sequentially: After understanding the theory for a puzzle type, practice similar or slightly higher difficulty puzzles to solidify learning.

Puzzle: Double Row Arrangement

This example involves two parallel rows with specific conditions, including alternating neighbors and relative positioning.

• Row 1 (Facing South): J, K, L, M, N

• Row 2 (Facing North): P, Q, R, S, T

Puzzle Conditions

1. R is third from the right end of the row.

2. Only one person sits between R and S.

3. The person opposite S faces one of the individuals from the South-facing row.

4. There are three people between the person opposite Q and the individual represented as 'J'.

5. Q is not an immediate neighbor of R or P.

6. J sits opposite T.

7. Only one person sits between M and L.

8. L and N are immediate neighbors.

9. The number of people sitting to the right of L is the same as the number of people sitting to the left of the person who faces P.

10. K sits to the left of M.

11. M sits opposite to R.

12. N is not an immediate neighbor of M.

Step-by-Step Solution and Deductions

1. Initial Placement & Case Creation: R is third from the right end in the North-facing row. "Only one person sits between R and S" creates two cases: S to the right of R or S to the left of R.

2. Placing M: Use "M sits opposite to R" to place M in Row 1, directly opposite R in both cases.

3. Case Elimination: Consider the case where S is to the right of R. With M opposite R, and conditions like "one person sits between M and L," "L and N are immediate neighbors," and "K sits to the left of M," this case quickly becomes contradictory as K cannot be placed to the left of M under these constraints. Thus, Case 1 is cancelled.

4. Developing the Correct Case (S to the left of R):

• Since Q cannot be a neighbor of R or P, P must be at the leftmost end of Row 2.

• The person facing P is at the rightmost end of Row 1. The number of people to the left of this person is 4.

• From condition 9: "The number of people sitting to the right of L is the same as the number of people sitting to the left of the person who faces P." This implies there should be 4 people to the right of L. This places L at the leftmost end of Row 1.

• With M and L determined (and one person between them), and knowing K is to M's left, K's position is fixed.

• N is a neighbor of L but not of M, finalizing N's position.

• The only person left in Row 1 is J, who takes the last remaining spot.

• The only person left in Row 2 is T. "J sits opposite T" (as 'U' was a placeholder for T).

Final Arrangement

• Row 1 (South): J, N, M, L, K

• Row 2 (North): P, T, Q, S, R

Answering the Question

• Question: Who sits opposite the person who is second to the right of J?

• Explanation: In the final South-facing row (J, N, M, L, K), the person second to the right of J is M. The person sitting opposite M in the North-facing row is R.

• Answer: R.