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Linear Arrangement (Two Rows)

Introduction

Two-row linear arrangements में लोग दो parallel rows में बैठते हैं और एक-दूसरे की ओर या विपरीत दिशा में face करते हैं। ये puzzles spatial reasoning, direction sense और relative positioning skills को परखते हैं।

यह पैटर्न higher-level reasoning में बहुत common है, खासकर banking और government exams में, जहाँ opposite-facing clues को सही तरह से संभालना ज़रूरी होता है।

Pattern: Linear Arrangement (Two Rows)

Pattern

Key Concept: पहले एक row fix करें, फिर “facing direction” के अनुसार opposite row के left/right को सही तरह interpret करें। जब दो rows एक-दूसरे की ओर face करती हैं:

  • Row 1 (facing South) → Left/Right observer के view से उलटे होते हैं।
  • Row 2 (facing North) → Left/Right observer के view जैसे ही होते हैं।

Step-by-Step Example

Question

आठ लोग दो parallel rows में बैठते हैं, हर row में चार लोग, और दोनों rows एक-दूसरे की ओर face करती हैं।
Row 1 (facing South): A, B, C, D
Row 2 (facing North): P, Q, R, S

Clues:
1️⃣ A, B के तुरंत left में बैठा है।
2️⃣ C, B के right में दूसरे स्थान पर है।
3️⃣ P, B के opposite बैठा है।
4️⃣ S, Row 2 के extreme right end पर बैठा है।

C के opposite कौन बैठा है?

Options:

  • A) P
  • B) Q
  • C) R
  • D) S

Solution

  1. Step 1: Fix Row 1 first

    A, B के तुरंत left में है → [A B]. C, B के right में दूसरे स्थान पर है → पैटर्न [A B C D] फिट होता है।

  2. Step 2: Apply opposite clue

    P, B के directly opposite बैठेगा → Row 2 में P को B के सामने रखें।

  3. Step 3: Apply Row 2 clue

    S, Row 2 के extreme right end पर होगा।

  4. Step 4: Fill remaining Row 2 positions

    बाकी Q और R positions 1 और 3 में बैठेंगे। Row 1 में C तीसरी position पर है, इसलिए उसका opposite Row 2 की तीसरी seat होगी → R.

  5. Final Answer:

    R → Option C

  6. Quick Check:

    Top row (A B C D) और bottom row (Q P R S) सभी clues satisfy करते हैं। ✅

Quick Variations

  • 1. दोनों rows एक ही दिशा में face कर रही हों (tricky - opposites flip हो जाते हैं)।
  • 2. दोनों rows में लोगों की संख्या unequal हो (पहले blanks भरें)।
  • 3. Cross-reference clues जैसे “X sits to the left of Y’s opposite.”

Trick to Always Use

  • Step 1 → दो parallel lines बनाकर दोनों rows के लिए columns 1-n mark करें।
  • Step 2 → adjacency/distance clues से पहले एक row पूरी तरह भरें।
  • Step 3 → opposite-facing row को column mapping से भरें।
  • Step 4 → final करने से पहले हर left/right को facing direction के अनुसार check करें।

Summary

Summary

  • पहले एक row को distance और adjacency clues से anchor करें।
  • left/right को हर व्यक्ति की facing direction के अनुसार interpret करें।
  • Opposites को column-by-column vertically map करें।
  • सभी positional और facing-direction clues को cross-verify करें।

याद रखने योग्य उदाहरण:
यदि Row 1 = A B C D और Row 2 = Q P R S, तब B ↔ P, C ↔ R.

Practice

(1/5)
1. Eight people are seated in two parallel rows of four each facing each other. Top row (Row-1, left→right): A, B, C, D. Bottom row (Row-2, left→right) are four of P, Q, R, S. It is known that P sits opposite A, Q sits immediately right of P (bottom-row view), and S sits at the extreme right of Row-2. Who sits opposite C?
easy
A. R
B. P
C. Q
D. S

Solution

  1. Step 1: Fix Row-1

    Top row columns 1-4: A, B, C, D.

  2. Step 2: Place P opposite A

    P opposite A → P in bottom col1.

  3. Step 3: Place Q and S

    Q immediate right of P (bottom view) → Q in bottom col2. S at extreme right → S in bottom col4.

  4. Step 4: Fill remaining bottom seat

    Remaining person R goes to bottom col3 → bottom row = P, Q, R, S (cols1-4).

  5. Final Answer:

    R → Option A

  6. Quick Check:

    Opposites: A↔P (col1), B↔Q (col2), C↔R (col3), D↔S (col4) ✅
Hint: Place fixed opposite pairs first, then apply same-row adjacency and end clues.
Common Mistakes: Interpreting 'right' relative to observer instead of the person's facing direction.
2. Ten people sit in two rows of five each facing each other. Top row (Row-1, left→right): A, B, C, D, E. Bottom row (Row-2, left→right) include P, Q, R, S, T. If P sits opposite C, Q sits immediate right of P (bottom view), S sits opposite A, and T sits at extreme right of Row-2, who is opposite D?
easy
A. T
B. R
C. Q
D. P

Solution

  1. Step 1: Fix Row-1 columns

    Top row columns 1-5: A, B, C, D, E.

  2. Step 2: Place P opposite C and S opposite A

    P opposite C → P in bottom col3. S opposite A → S in bottom col1.

  3. Step 3: Place Q relative to P and T at end

    Q immediate right of P (bottom view) → Q in bottom col4. T at extreme right → T in bottom col5.

  4. Step 4: Fill remaining slot

    Remaining bottom person R goes to bottom col2 → bottom row = S, R, P, Q, T → opposite of D (col4) = Q.

  5. Final Answer:

    Q → Option C

  6. Quick Check:

    P opposite C (col3) ✅ Q right of P (col4) ✅ S opposite A (col1) ✅ T extreme right (col5) ✅ → Opposite D = Q ✅
Hint: Place opposites and end seats first, then fill adjacency slots and leftovers.
Common Mistakes: Placing adjacency in bottom row without first fixing opposite constraints.
3. Eight people sit in two rows (4 each) facing each other. Top row (left→right): G, H, I, J. Bottom row (left→right) are K, L, M, N. Clues: K sits opposite H; L sits immediate left of K (bottom view); N sits opposite J; M is not at any end. Who sits opposite I?
easy
A. K
B. L
C. N
D. M

Solution

  1. Step 1: Fix top row

    Top row cols1-4 = G, H, I, J.

  2. Step 2: Place K opposite H

    K opposite H → K in bottom col2.

  3. Step 3: Place L left of K and N opposite J

    L immediate left of K (bottom view) → L in bottom col1. N opposite J → N in bottom col4.

  4. Step 4: Place M (not at any end)

    Remaining bottom slot is col3 → M in col3. Bottom row = L, K, M, N.

  5. Step 5: Opposite of I

    I is top col3 → opposite = M.

  6. Final Answer:

    M → Option D

  7. Quick Check:

    Bottom row L (col1), K (col2), M (col3), N (col4): K opposite H ✅ L left of K ✅ N opposite J ✅ M not at end (col3) ✅ → Opposite I = M ✅
Hint: After placing opposites and adjacency, the remaining non-end person usually occupies the lone middle slot.
Common Mistakes: Placing the non-end person at an end before checking adjacency constraints.
4. Eight persons sit in two rows of four each facing each other. Row-1 (left→right) has M, N, O, P. In Row-2 (left→right) are A, B, C, D. If A is opposite N, B is immediate left of A (bottom-row view), C is opposite O, and D is at the extreme right of Row-2, who is immediate right of B?
medium
A. A
B. C
C. D
D. None

Solution

  1. Step 1: Fix Row-1

    Top row cols1-4 = M, N, O, P.

  2. Step 2: Place A opposite N and C opposite O

    A opposite N → A in bottom col2. C opposite O → C in bottom col3.

  3. Step 3: Place B and D

    B immediate left of A (bottom view) → B in bottom col1. D at extreme right → D in bottom col4. Final bottom row = B, A, C, D.

  4. Step 4: Immediate right of B

    Immediate right of B (col1) is A (col2) → A.

  5. Final Answer:

    A → Option A

  6. Quick Check:

    Bottom row B (col1), A (col2), C (col3), D (col4) gives A opposite N (col2) ✅ B left of A ✅ C opposite O ✅ D at extreme right ✅
Hint: If adjacency and end constraints conflict, place adjacency first then fit ends into remaining slots.
Common Mistakes: Locking end seats too early before placing adjacency clues.
5. Twelve people sit in two rows of six each facing each other. Top row (Row-1 left→right): W, X, Y, Z, U, V. Bottom row (Row-2 left→right) are P, Q, R, S, T, O. If Q is opposite X, R is immediate left of Q (bottom view), S is opposite Z, and P is at extreme right, who is opposite U?
medium
A. O
B. T
C. R
D. P

Solution

  1. Step 1: Fix Row-1 columns

    Cols1-6 (left→right) = W, X, Y, Z, U, V.

  2. Step 2: Place Q opposite X and R left of Q

    Q opposite X → Q in bottom col2. R immediate left of Q (bottom view) → R in bottom col1.

  3. Step 3: Place S opposite Z and P at extreme right

    S opposite Z → S in bottom col4. P at extreme right → P in bottom col6.

  4. Step 4: Fill remaining bottom slots

    Remaining bottom persons T and O occupy col3 and col5. Assign col5 = T and col3 = O. Bottom row = R, Q, O, S, T, P → opposite of U (col5) = T.

  5. Final Answer:

    T → Option B

  6. Quick Check:

    Q opposite X (col2) ✅ R left of Q (col1) ✅ S opposite Z (col4) ✅ P at col6 ✅ → Opposite U (col5) = T ✅
Hint: Place fixed opposites and end seats first; remaining persons fill middle columns.
Common Mistakes: Assuming bottom-row left/right relative to observer rather than each person's facing.

Mock Test

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