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Ranking & Order

Reasoning Ability · Core Logical Tools

Useful for: SSC CGL, Railway RRB, IBPS Banking, OSSC RHT — Regular High School Teacher, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Arts, OSEPA Upper Primary — Science, OSSSC Govt Physical Education Teacher (PET)

and 3 more exams

OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM

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Overview

Ranking items use the identity total = rank from one end + rank from the other end − 1, plus careful handling of positions between people.

Key points

Total in a row = left rank + right rank − 1.
Rank from the other end = total − rank + 1.
People between A and B (same side counts) = difference in ranks − 1.
If A is p-th from the left and B q-th from the right in a row of n, and they do not overlap, people between = n − p − q.
Interchange questions: use the changed rank to find the total.

Explanation

Check whether the two people’s positions overlap (crossed) before using n − p − q.
For arrangement by height or marks, write the order as a chain (A > B > C).
Minimum number of people: allow positions to overlap where possible.
"Top" and "bottom" are like "left" and "right".

Step by step

Write the ranks.
Apply the formula.
Check overlap and verify.

Examples

Ravi is 12th from the top and 20th from the bottom → 12 + 20 − 1 = 31 students.
In a row of 40, A is 10th from the left and B is 15th from the right → people between = 40 − 10 − 15 = 15.
Riya is 7th from the left in a row of 25 → 25 − 7 + 1 = 19th from the right.

Traps and advanced points

Trap: Forgetting the "− 1" in the total.
Trap: Using n − p − q when positions overlap.
Trap: Mixing left and right ranks.

Quick revision

Total = L + R − 1.
Other-end rank = n − r + 1.
Between = n − p − q (no overlap).

Practice MCQs

In a row of 69 students, Riya is 43th from the left. What is her rank from the right?
1. 33
2. 24
3. 27
4. 30
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Answer: (c) 27. Right rank = total − left rank + 1.
In a row of 80 students, Riya is 21th from the left. What is her rank from the right?
1. 66
2. 57
3. 60
4. 63
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Answer: (c) 60. Right rank = total − left rank + 1.
In a row of 91 students, Riya is 54th from the left. What is her rank from the right?
1. 41
2. 38
3. 44
4. 35
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Answer: (b) 38. Right rank = total − left rank + 1.
In a row of 102 students, Riya is 87th from the left. What is her rank from the right?
1. 19
2. 22
3. 16
4. 13
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Answer: (c) 16. Right rank = total − left rank + 1.
In a row of 113 students, Riya is 21th from the left. What is her rank from the right?
1. 93
2. 90
3. 99
4. 96
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Answer: (a) 93. Right rank = total − left rank + 1.
In a row of 63 students, Riya is 19th from the left. What is her rank from the right?
1. 42
2. 45
3. 51
4. 48
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Answer: (b) 45. Right rank = total − left rank + 1.
In a row of 74 students, Riya is 63th from the left. What is her rank from the right?
1. 18
2. 9
3. 12
4. 15
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Answer: (c) 12. Right rank = total − left rank + 1.
In a row of 85 students, Riya is 36th from the left. What is her rank from the right?
1. 47
2. 56
3. 50
4. 53
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Answer: (c) 50. Right rank = total − left rank + 1.
In a row of 96 students, Riya is 69th from the left. What is her rank from the right?
1. 34
2. 31
3. 28
4. 25
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Answer: (c) 28. Right rank = total − left rank + 1.
In a row of 107 students, Riya is 9th from the left. What is her rank from the right?
1. 99
2. 105
3. 102
4. 96
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Answer: (a) 99. Right rank = total − left rank + 1.
In a row, Ravi is 7th from the left and 9th from the right. How many persons are in the row?
1. 14
2. 17
3. 15
4. 16
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Answer: (c) 15. Formula: Left + Right - 1 = 7 + 9 - 1 = 15.
In a class of 40, Sita's rank is 12th from the top. Her rank from the bottom is:
1. 29th
2. 28th
3. 30th
4. 27th
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Answer: (a) 29th. Rank from bottom = Total - rank from top + 1 = 40 - 12 + 1 = 29th.
A is taller than B, C is taller than A, D is shorter than B. Who is the tallest?
1. A
2. B
3. D
4. C
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Answer: (d) C. C>A>B>D (arrange in order).
In a queue, Mohan is 10th from front and 25th from back. Total persons in queue:
1. 33
2. 36
3. 34
4. 35
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Answer: (c) 34. Total = front + back - 1 = 10 + 25 - 1 = 34.
Five girls A, B, C, D, E. A is shorter than B but taller than E. C is the tallest. D is between A and B. The shortest is:
1. E
2. A
3. D
4. B
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Answer: (a) E. C>B>D>A>E.