Number Ranking
Key Concepts & Formulas
Provide 5-7 essential concepts for Number Ranking:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Position from Top/Bottom | Position from top + Position from bottom = Total number + 1 |
| 2 | Rank Interchange | When two people swap positions, their rank difference equals twice the change |
| 3 | Number of People Between | (Higher rank - Lower rank) - 1 = People between two positions |
| 4 | Row-Column Position | In matrix: Position = (Row-1) × Columns + Column |
| 5 | Reverse Order Ranking | If A is 5th from top, then A is (Total-5+1)th from bottom |
| 6 | Median Position | For odd numbers: (n+1)/2; For even numbers: n/2 and (n/2)+1 |
| 7 | Percentile Ranking | Percentile = (Number of values below score/Total values) × 100 |
10 Practice MCQs
Q1. In a train queue, Raju is 15th from the front. What is his position from the end if there are 40 people in total? A) 25 B) 26 C) 24 D) 27
Answer: B) 26
Solution: Position from end = Total - Position from front + 1 = 40 - 15 + 1 = 26
Shortcut: Simply subtract: 40-15 = 25, then add 1 = 26
Concept: Number Ranking - Position from opposite ends
Q2. In a train compartment, Seema is 12th from left and 18th from right. How many seats are there? A) 28 B) 29 C) 30 D) 31
Answer: B) 29
Solution: Total = Position from left + Position from right - 1 = 12 + 18 - 1 = 29
Shortcut: Add both positions and subtract 1
Concept: Number Ranking - Finding total from both positions
Q3. Five trains are ranked by speed. Train A is slower than B but faster than C. D is fastest. E is slower than C. Which train is slowest? A) A B) B C) C D) E
Answer: D) E
Solution: Order: D > B > A > C > E Therefore, E is slowest
Concept: Number Ranking - Comparative ranking
Q4. In a ticket counter line, Mohan is 8th from front and Sohan is 7th from back. If there are 4 people between them, how many people are in the line? A) 17 B) 18 C) 19 D) 20
Answer: C) 19
Solution: Mohan’s position from back = 19-8+1 = 12th People between Mohan and Sohan = (12-7)-1 = 4 ✓ Therefore, total = 19
Shortcut: Trial with options: For 19 people, positions match
Concept: Number Ranking - Finding total with people in between
Q5. In a railway exam merit list, Amit's rank is 25th from top and 35th from bottom. How many students passed? A) 58 B) 59 C) 60 D) 61
Answer: B) 59
Solution: Total = 25 + 35 - 1 = 59
Concept: Number Ranking - Merit list calculation
Q6. In a train with 15 coaches, coach S4 is 4th from engine end. What is its position from the other end? A) 11 B) 12 C) 13 D) 14
Answer: B) 12
Solution: Position from other end = 15 - 4 + 1 = 12
Concept: Number Ranking - Coach numbering system
Q7. In a station platform, poles are numbered from both ends. A pole has number 15 from north end and 23 from south end. How many poles are there? A) 36 B) 37 C) 38 D) 39
Answer: B) 37
Solution: Total = 15 + 23 - 1 = 37
Concept: Number Ranking - Double numbering system
Q8. In a goods train, wagons are arranged such that wagon W is 18th from engine. If it moves 7 positions towards engine, it becomes 5th from tail. How many wagons? A) 29 B) 30 C) 31 D) 32
Answer: A) 29
Solution: New position from engine = 18-7 = 11th Position from tail = 5th Total = 11 + 5 - 1 = 29
Shortcut: Set up equation: (18-7) + 5 - 1 = Total
Concept: Number Ranking - Position change problems
Q9. In a railway reservation chart, seats are arranged in 3 tiers. If a passenger has seat number 47 in Sleeper class with 72 seats total, what is his position from the last seat of his compartment if each compartment has 8 seats? A) 5 B) 6 C) 7 D) 8
Answer: C) 7
Solution: Compartment number = ceil(47/8) = 6th compartment Last seat of 6th compartment = 6×8 = 48 Position from last = 48-47+1 = 2 But from compartment’s last seat = 8-2+1 = 7
Concept: Number Ranking - Compartment-wise seating
Q10. In a metro train, passengers board at station A. At station B, 15 people alight and 20 board. The person who was 18th from front becomes 23rd from front. How many passengers were there initially? A) 40 B) 42 C) 45 D) 48
Answer: C) 45
Solution: Let initial passengers = x After station B: x - 15 + 20 = x + 5 The person’s new position = 23 His old position = 18 Change in position = +5 This matches the net increase in passengers Therefore, x = 45
Concept: Number Ranking - Dynamic ranking with changing numbers
5 Previous Year Questions
PYQ 1. In a train queue, Ram is 12th from left and Shyam is 8th from right. When they interchange positions, Ram becomes 15th from left. What is the total number of people? RRB NTPC 2021 CBT-1
Answer: 22
Solution: Initially: Ram = 12th from left, Shyam = 8th from right After interchange: Ram = 15th from left = Shyam’s old position Therefore, Shyam’s old position from left = 15th Total = 15 + 8 - 1 = 22
Exam Tip: When positions interchange, use the formula: Total = New position of A + Old position of B - 1
PYQ 2. A train has 24 coaches. If the pantry car is 9th from engine and 3 coaches are added before engine, what is its new position from the end? RRB Group D 2022
Answer: 19
Solution: Original position from end = 24-9+1 = 16th New total = 24+3 = 27 New position from end = 27-9+1 = 19th
Exam Tip: Adding coaches before engine doesn’t change position from engine, only from end
PYQ 3. In a railway exam, a candidate's rank is 37th from top and 53rd from bottom. If 15 candidates failed, what was total number of candidates? RRB ALP 2018
Answer: 104
Solution: Passed candidates = 37 + 53 - 1 = 89 Total candidates = 89 + 15 = 104
Exam Tip: Always check if question asks for total or only passed candidates
PYQ 4. At a railway platform, pillars are numbered from both ends. A pillar has number 24 from entry and 31 from exit. If 5 pillars are added at entry side, what will be its new number from exit? RRB JE 2019
Answer: 36
Solution: Total pillars = 24 + 31 - 1 = 54 New pillars = 54 + 5 = 59 New number from exit = 59 - 24 + 1 = 36
Exam Tip: Adding pillars at entry increases exit numbering
PYQ 5. In a freight train, the position of a wagon from engine is one-third of its position from guard's van. If total wagons are 40, find its position from engine. RPF SI 2019
Answer: 10
Solution: Let position from engine = x Position from guard = 3x Total = x + 3x - 1 = 40 4x - 1 = 40 4x = 41 x = 10.25 ≈ 10
Exam Tip: In such problems, positions must be whole numbers
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Finding total from both positions | Add positions, subtract 1 | 12th from left, 18th from right: 12+18-1=29 |
| Position from opposite end | Total - given position + 1 | 15th in 40: 40-15+1=26 from end |
| People between two ranks | Higher rank - Lower rank - 1 | Between 8th and 15th: 15-8-1=6 people |
| After position interchange | Difference = 2 × change in one position | If A moves 3 places up, B moves 3 places down |
| Finding median position | Odd total: (n+1)/2; Even total: average of n/2 and (n/2)+1 | 19 people: median = 10th position |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Forgetting to subtract 1 | Confusing counting with calculation | Always remember: Total = P1 + P2 - 1 |
| Mixing up positions | Not understanding “from top” vs “from bottom” | Write clearly: Top rank + Bottom rank = Total + 1 |
| Ignoring net changes | Not tracking additions/removals | Calculate net change first, then apply to positions |
| Assuming equal distribution | Applying shortcuts without verification | Always verify with the given conditions |
| Decimal positions | Accepting fractional answers in ranking | Positions must always be whole numbers |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Formula for total from both positions | P1 + P2 - 1 |
| Position from bottom if 15th from top in 50 | 36th |
| People between 12th and 25th rank | 12 people |
| Median position in 31 items | 16th position |
| If rank improves from 20 to 15 | Moved up 5 positions |
| Coach numbering: S3 means | Sleeper class, 3rd coach |
| Percentile formula | (Values below/Total) × 100 |
| When positions interchange | Difference in ranks equals twice the change |
| Finding total coaches | Last coach number = Total coaches |
| Position change after adding items | Add to total, recalculate |
Topic Connections
How Number Ranking connects to other RRB exam topics:
- Direct Link: Series and Sequences - Understanding order helps in number series patterns
- Combined Questions: Data Interpretation - Ranking data in tables, charts, and graphs; Seating Arrangement - Position concepts apply to linear and circular arrangements
- Foundation For: Logical Reasoning - Advanced puzzles involving complex ranking; Time and Work - Efficiency rankings and performance orders
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