Syllabus Numbers & Quantification Locating the position of a person in a seating arrangement

Locating the position of a person in a seating arrangement

Comprehensive guide on locating positions in linear and circular seating arrangements, covering coordinate-based logic, indexing, and relative positioning for CBSE Class 11 Applied Mathematics.

Linear Seating Arrangement

In a linear arrangement, individuals are placed in a row. The position is determined by their index from the left or right extreme. If a row has 'n' people, the position of a person from the right can be derived from their position from the left.

Position from Right = (Total Number of People - Position from Left) + 1
Example 1: In a row of 20 students, Rahul is standing at the 7th position from the left. What is his position from the right?
Show Step-by-Step Solution

• Identify given values: Total (n) = 20, Position from left = 7.
• Apply the formula: Position from right = (20 - 7) + 1.
• Calculate: 13 + 1 = 14.

Answer: Rahul is at the 14th position from the right.

Circular Seating Arrangement

In circular arrangements, there is no fixed beginning or end. Positions are defined relative to others (to the immediate left or right). For a circle of 'n' people, moving 'k' positions clockwise or counter-clockwise requires modular arithmetic thinking.

New Position = (Current Position ± Shift) mod n
Example 1: Five people (A, B, C, D, E) are sitting around a circular table. If A is at position 1, who is sitting 2 places to the right of A (moving clockwise)?
Show Step-by-Step Solution

• Assign positions 1 to 5 in a clockwise direction.
• Start at position 1 (A).
• Move 2 places clockwise: 1 + 2 = 3.
• Identify the person at position 3.

Answer: The person at position 3 is sitting 2 places to the right of A.