Rank
Race ranks; queue position from both ends.
Rank
Rank and Queue Problems
What you'll learn
- Find rank from left/right in a queue.
- Use formula: Total = rank from left + rank from right − 1.
- Handle race finishing positions (1st, 2nd, 3rd).
- Solve double-ended queue puzzles.
Key concepts
Level 1 — Rank in queue
In a line, Meera is 4th from the left and 6th from the right.
Total = 4 + 6 − 1 = 9 people.
Level 2 — Why subtract 1?
Meera is counted twice — once from each end.
Level 3 — Race rank
1st = winner; 2nd = one person finished before you.
Level 4 — Indian context
Cricket team queue for autographs in Chennai — find position from both ends.
NCERT anchor: CBSE Class 4 olympiad reasoning — race ranks and queue positions
Worked example
Ravi is 5th from left and 7th from right. How many in queue?
Step 1 — Total = 5 + 7 − 1.
Step 2 — 12 − 1 = 11.
Answer: **11 people**
In a race of 10 runners, Amit finished 3rd. How many finished after him?
Step 1 — 3rd means 2 finished before.
Step 2 — After him: 10 − 3 = 7.
Answer: **7 runners**
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Total = left + right (no −1) | Double counting person | Always subtract 1 |
| 1st rank means one person behind | Off-by-one in race | 1st → 0 ahead, everyone else behind |
| Confusing rank with count after | Rank 3 ≠ 3 behind | 3rd of 10 → 7 behind |
| Left and right swapped | Misreading direction | Label left and right on diagram |
Quick check
- 4th from left, 5th from right — total?
- 10 runners, rank 1 — how many after?
- Formula for total in queue?
- Stretch: In a queue of 25, Karan is 10th from left. What is his rank from the right?
Revision tip: Memorise: Total = L + R − 1 — draw dots and count to see why −1 is needed.
Open the Practice tab for graded questions on Rank and Queue Problems.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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