SATHEE: Ranking Arrangement

Ranking Arrangement – Quick Revision

Position = place from Top/Left/Start; Rank = place from Bottom/Right/End.
Total students = (Rank from top + Rank from bottom) – 1.
Rank from top = (Total + 1) – Rank from bottom.
In a row of n persons, the k-th from left has (n – k + 1) from right.
After interchanging positions, the total remains unchanged – use it to find unknowns.
Overlapping ranks ⇒ subtract the overlap once: Total = Sum – Common.
When A is left of B, their positions are not necessarily consecutive – check for gaps.
In circular/closed loop, clockwise & anti-clockwise ranks add up to (total + 1).
Always draw a horizontal line & place given positions first – visualise gaps.
“Between” means strictly in the middle – count neither of the two extremes.
If two people interchange & new ranks are given, the difference of their old ranks equals the difference of their new ranks.
For double-row (2 parallel rows), map face-to-face pairs: 1st of row-1 faces 1st of row-2, etc.
Shortcut: “T + B – 1 = Total” – write on margin when you see top & bottom ranks.
When same rank is mentioned from both sides ⇒ person is exactly mid; total must be odd.
Speed-tip: After placing 3 fixed positions, calculate remaining gaps in one equation.

Formula / Rule	What it Solves
Total = (Top Rank + Bottom Rank) – 1	Classic single-row unknown total
Top Rank = (Total + 1) – Bottom Rank	Convert bottom to top rank
Gap between A & B =	PositionA – PositionB
New rank after swap = Old rank ± (shift amount)	Interchange problems
Mid-position = (Total + 1) / 2	Find exact middle person
Left rank = (Total + 1) – Right rank	Horizontal row symmetry
Clockwise rank = (Total + 1) – Anti-clockwise rank	Circular table symmetry
Double-row pair: (i-th left of row-1) faces (i-th right of row-2)	Parallel rows
Sum of ranks from two ends for same person = Total + 1	Quick cross-check

“T+B-1” sounds like “Tea plus coffee minus one” – total people in queue.
“Top from Bottom, Bottom from Top – flip with plus one” – rank conversion.
Draw “stick-figure queue” in 5 s: horizontal line + 3 arrows – prevents silly counting.
“Swap = Same Sum” – when two interchange, their rank-sum remains same (Total + 1).
Odd total → middle person exists; Even total → middle pair – decide quickly.

Mistake	Correct Approach
Counting the overlap person twice	Subtract 1 in “sum of two ranks” formula
Forgetting (+1) while converting top ↔ bottom rank	Remember: (Total + 1) is the mirror
Assuming “between” includes end persons	Strictly (Position diff – 1)
Mixing left & right directions in circular	Fix clockwise as +1 direction once
Ignoring interchange gives two equations	Write old & new rank for both persons

10 s sketch: Draw row & mark known positions – saves 1 min of re-reading.
First check parity (odd/even total) – eliminates two options in MCQs instantly.
If two ranks given (top & bottom) → direct formula – don’t count on fingers.
Swap problems: write old rank, new rank, shift in three columns – clarity in 5 s.
Double-row: label rows Row-I & Row-II below rough figure – prevents left-right confusion.

1. In a row of 40 students, A is 13th from left. What is his position from right end?

> **Sol.** (40 + 1) – 13 = 28th. > **Ans.** 28th

2. Ram is 18th from either end of the row. How many students are there?

> **Sol.** Total = (18 + 18) – 1 = 35. > **Ans.** 35

3. After interchanging seats, Rohan’s rank becomes 9th from 15th (left). Earlier he was 7th from left. Total students?

> **Sol.** Shift = 15 – 9 = 6. Old rank 7 → new rank 7 + 6 = 13th (given 9th) contradiction ⇒ shift = 6 ⇒ total = (15 + 9) – 1 = 23. > **Ans.** 23

4. In a circular arrangement of 25 people, what is the rank of the person exactly opposite the 8th clockwise?

> **Sol.** Opposite rank = (25 / 2) + 8 = 12.5 + 8 = 20.5 → 20th or 21st. Since integer, (8 + 12) mod 25 = 20th. > **Ans.** 20th

5. Two parallel rows of 10 each face each other. 3rd from left in Row-1 faces which position in Row-2?

> **Sol.** 3rd from left in Row-1 ↔ 3rd from right in Row-2 = (10 + 1) – 3 = 8th. > **Ans.** 8th from left in Row-2