Ranking & Order

Subject: Reasoning | Frequency: 1-2 questions per APPSC paper | Time: 30-45 sec/question

Introduction

Ranking questions involve positions in a row, class, or queue. You must find total count, convert rank from one end to another, or count people between two positions. The formula T = L + R - 1 (Total = rank from Left + rank from Right - 1) is the single most important formula and solves 80%+ of ranking questions.

Core Method

1. Identify what's given — rank from top/left, rank from bottom/right, total
2. Identify what's asked — convert, count between, find total
3. Apply the appropriate formula
4. Check for overlap — when two positions are given, verify they could be the same or different person
5. Verify — answer must be a positive integer

Key Formulas

Worked Examples — Easy

Q1: In a class of 46 students, Anita ranks 12th from top. What is her rank from bottom?

• Rank from bottom = Total - Rank from top + 1
• = 46 - 12 + 1 = 35th

Q2: Rakesh ranks 7th from top and 28th from bottom. How many students in class?

• Total = 7 + 28 - 1 = 34 students

Q3: In a row of 40 children, Manu is 13th from the left. Position from right?

• Position from right = 40 - 13 + 1 = 28th

Worked Examples — Medium

Q4: Ravi is 7 ranks ahead of Sumit in a class of 39. Sumit is 17th from last. Ravi's rank from start?

• Sumit's rank from start = 39 - 17 + 1 = 23rd
• "7 ranks ahead" = lower rank number = 23 - 7 = 16th from start

Q5: Shilpa is 8th from left, Reena is 17th from right. After interchange, Shilpa becomes 14th from left. Total girls?

• After interchange: Shilpa now at Reena's original position
• Shilpa's new position from left = 14
• Reena's original position from right = 17
• Total = 14 + 17 - 1 = 30 girls

Q6: Mohan is 15th from left. Sohan is 20th from right. 8 people between them. Total? (non-overlapping)

• Total = 15 + 20 + 8 = 43
• (Alternative if overlapping: 15 + 20 - 8 - 2 = 25 — check which answer appears in options)

Worked Examples — Hard

Q7: Manish ranks 16th from top and 29th from bottom among passed students. 6 boys didn't participate; 5 failed. Total boys in class?

• Passed = 16 + 29 - 1 = 44
• Total = Passed + Failed + Non-participants = 44 + 5 + 6 = 55

Q8: Five friends: Mohan older than Prabir. Suresh younger than Prabir. Mihir older than Suresh but younger than Prabir. Ram is youngest.

• Order (oldest to youngest): Mohan > Prabir > Mihir > Suresh > Ram
• Middle position: Mihir

Q9: In a row of 50 people, A is 20th from left, B is 30th from right. People between A and B?

• B from left = 50 - 30 + 1 = 21
• A at 20, B at 21 → adjacent
• People between = 0

Shortcuts & Tricks

Common Mistakes

1. Forgetting the -1 — Total = Top + Bottom - 1 (not just Top + Bottom)
2. "Ahead" direction — "7 ranks ahead" from position 23 = position 16 (subtract, not add)
3. Overlap vs non-overlap — must check if two people's positions overlap or not
4. Mixing left-right with top-bottom — same formulas apply, but keep terminology consistent
5. Not checking integer results — if the answer isn't a whole number, recheck your setup

Exam Strategy

• Memorize T = L + R - 1 and position conversion — these two solve 80%+ of questions
• APPSC keeps difficulty at easy-to-medium
• Time: 30-45 seconds per question
• For "between" questions, always check if two people could be the same person (overlap)
• Negative marking: -0.333 — formula-based questions give very high confidence

Practice Questions

1. Class of 30, Rani is 10th from top. Rank from bottom? → 30 - 10 + 1 = 21st
2. 5th from left and 18th from right. Total? → 5 + 18 - 1 = 22
3. Class of 45, 12th from top and 26th from bottom. Same person? → 12 + 26 - 1 = 37 (not 45, so different person)
4. A is 15th from left in row of 50. B is 20th from right. Between them? → B from left = 31. Between = 31 - 15 - 1 = 15
5. Rank from top = 3x rank from bottom, total = 61. Rank from bottom? → 3x + x - 1 = 61, 4x = 62, x = 15.5 (not integer → check question)

Key Terms / Formulas