Linear Arrangement is one of the most frequently tested puzzle types in IBPS PO Prelims, appearing in almost every exam with 3–5 questions per set. The concept is straightforward: arrange persons in one or two straight rows based on given conditions about their positions and the direction they face.
This topic forms the foundation for all seating arrangement problems. Mastering linear arrangement builds the logical framework you need for circular and rectangular puzzles. In IBPS PO Prelims, expect one full set (5 questions) from either linear or circular arrangement — sometimes both. The difficulty ranges from moderate to high, with double-row arrangements being trickier than single-row.
To score well, you must develop a systematic approach: fix one person first, use definite clues before vague ones, and always mark facing directions clearly. Speed comes from practice — aim to solve a 5-question set in under 7 minutes.
Key Concepts
**Single Row Arrangement**: All persons sit in one straight line, either facing North (standard assumption) or facing South. Left-right positions are determined from the perspective of the persons sitting.
**Double Row Arrangement**: Two parallel rows where Row 1 faces Row 2. Typically, one row faces North and the other faces South. "Facing each other" means directly opposite.
**Left and Right Convention**: Always determine left/right from the sitting person's perspective, not from your viewing angle. If a person faces North, their left is towards West; if facing South, their left is towards East.
**Immediate Neighbours**: Persons sitting directly adjacent (no gap between them). "A sits to the immediate left of B" means A is exactly one position to B's left.
**"Between" vs "Exactly Between"**: "A sits between B and C" means A is somewhere in the middle portion. "A sits exactly between B and C" means A is equidistant from both.
**Opposite Positions in Double Row**: In a double-row setup with equal persons in each row, "A faces B" means they are in the same column position in their respective rows.
**End Positions**: The extreme left and extreme right seats. Persons at ends have only one neighbour.
Formulas / Key Facts
**Total positions in single row** = Number of persons (each person occupies exactly one seat)
**Position from opposite end** = Total persons + 1 − Position from given end
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**Gap between two persons** = |Position of A − Position of B| − 1
In double-row facing each other: if Row 1 faces North, their left is West; Row 2 faces South, their left is East
"A and B are neighbours" = A and B sit adjacent (one position apart)
"A sits second to the left of B" = One person sits between A and B, with A on the left side
"Not adjacent" or "not immediate neighbour" = At least one person between them
When rows face each other, if A faces B, then B also faces A (symmetric relationship)
Worked Examples
**Example 1: Single Row**
*Eight persons P, Q, R, S, T, U, V, W sit in a row facing North. R sits third from the left end. T sits second to the right of R. Q sits at the extreme right. S sits exactly between R and T. Only two persons sit between T and Q.*
**Solution**:
Place R at position 3 from left
T is second to right of R → T at position 5
S is exactly between R and T → S at position 4
Q is at extreme right → Q at position 8
Two persons between T and Q → Positions 6 and 7 are occupied (T at 5, Q at 8 — positions 6, 7 between them) ✓
Arrangement so far: _ _ R S T _ _ Q Remaining: P, U, V, W for positions 1, 2, 6, 7
**Example 2: Double Row**
*Six persons A, B, C, D, E, F sit in two rows of three each. Row 1 faces South; Row 2 faces North (so they face each other). A sits at one of the ends of Row 1. B faces A. C sits to the immediate right of B. E does not face C.*
**Solution**:
Row 1: _ _ _ (facing South, so their left is East)
Row 2: _ _ _ (facing North, so their left is West)
A is at an end of Row 1 → A at position 1 or 3 of Row 1
B faces A → B is in Row 2, directly opposite A
C is immediate right of B → C is one position to B's right (from B's perspective facing North)
If A is at left end of Row 1, B is opposite in Row 2. C to B's right (B faces North, right = East direction).
Continue placing D, E, F using remaining clues.
**Example 3: Position Calculation**
*In a row of 15 persons, A is 7th from the left. B is 5th from the right. How many persons are between A and B?*
**Solution**:
A's position from left = 7
B's position from left = 15 − 5 + 1 = 11
Persons between A and B = 11 − 7 − 1 = 3
Common Mistakes
**Confusing left-right based on your view vs person's view** → Always determine left/right from the sitting person's facing direction, not from how you see the diagram.
**Ignoring facing direction in double rows** → In double-row problems, left-right reverses between rows because they face opposite directions. Draw arrows to mark facing direction.
**Assuming "second to the left" means two gaps** → "Second to the left of B" means exactly one person between them, not two. Count positions, not gaps.
**Treating "between" as "exactly between"** → Unless the clue says "exactly" or "in the middle," the person could be anywhere in that segment with unequal distances.
**Not fixing definite positions first** → Starting with vague clues like "A does not sit at the end" leads to multiple trial cases. Always begin with concrete placements like "B sits third from left."
Quick Reference
Left/Right = Always from the seated person's perspective based on their facing direction
Position from other end = Total + 1 − Given position
Persons between A and B = |Position difference| − 1
Double row facing each other: Row 1 faces North → left is West; Row 2 faces South → left is East
"Immediate left/right" = Directly adjacent, no one between
Start with definite clues; save negative clues ("not adjacent," "does not face") for elimination