ORDER & RANKING – REASONING NOTES: For CUET | CLAT | IPMAT
ORDER & RANKING – REASONING NOTES:
For CUET | CLAT | IPMAT
1. BASIC CONCEPTS
Rank:
The position of a person/object in a sequence (from
Left/Right, Top/Bottom, Front/Back).
Types of Questions:
- Rank
from one side
- Finding
total number of persons
- Finding
opposite side rank
- Interchange
of positions
- Comparison-based
ranking
- Ranking
in a row/height/marks
- Complex
puzzles involving group arrangement
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TYPE 1: Finding Rank from Opposite Side
Formula:
If a person’s Left Rank = L and Right Rank = R,
then Total = L + R – 1
Example 1:
A is 7th from the left and 10th from the right. Find the
total number of students.
Solution:
Total = 7 + 10 – 1 = 16
Example 2:
In a row of students, Ravi is 15th from the left. If the
total strength is 40, find his rank from the right.
Right Rank = 40 – 15 + 1
= 26
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TYPE 2: Finding Total Number of Persons
Case 1: Rank from both ends of the SAME person
Use: Total = L + R – 1
Case 2: Rank from both ends of TWO different persons
Question:
A is 6th from the left, B is 9th from the right. There are 4 persons between A
and B. Find total number.
Formula:
Total = L(A) + R(B) + persons_between – 1
= 6 + 9 + 4 – 1 = 18
PYQ (CUET-style)
In a row, Seema is 12th from the left. Reena is 15th from
the right. If 6 students sit between them, find total strength.
Solution:
Total = 12 + 15 + 6 – 1 = 32
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TYPE 3: Finding Number of Persons Between Two People
Formula (Same Side Ranks):
If A is L(A)th from left & B is L(B)th from left,
Persons between = | L(A) – L(B) | – 1
Example:
A is 8th from the left. B is 14th from the left.
Persons between = |14 – 8| – 1 = 5
Formula (Opposite Side Given):
If total = T
A’s left rank = L
B’s right rank = R
Find persons between = T – (L + R)
Example:
Total = 30
A’s left rank = 10
B’s right rank = 12
Between = 30 – (10 + 12) = 8
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TYPE 4: Interchanging Positions
Concept:
When two persons interchange positions, their ranks also
interchange.
Example:
Rita is 9th from left, Sita is 15th from left. They
interchange places.
Find new rank of Rita.
Solution:
Rita will take Sita’s place = 15th
Sita will take Rita’s place = 9th
Example (Moderate):
In a row of 40, A is 6th from left and B is 11th from right.
They interchange positions. Now A is 20th from left. Find B’s new rank from
right.
Solution:
- Find
B’s original left rank:
Left rank of B = 40 – 11 + 1 = 30
After interchange, B moves to A’s initial left rank = 6th
B’s new right rank = 40 – 6 + 1 = 35
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TYPE 5: Ranking Based on Marks / Height / Weight
Case 1: Highest to Lowest Ranking
Example:
Marks of five students:
A = 76, B = 88, C = 90, D = 65, E = 76
Order (highest → lowest):
C (1st), B (2nd), A & E (3rd – tie), D (4th)
Case 2: Tie-Breaking
If two students have same marks → they get same rank.
Next rank is skipped.
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TYPE 6: Position of Person After Some Join/Leave
Example 1:
A is 12th from left in a row of 50.
5 more join on the left side.
Find new rank of A.
Solution:
New rank = 12 + 5 = 17
Example 2:
A is 10th from left out of 40.
If 3 persons ahead of him leave → his new rank:
New rank = 10 – 3 = 7
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TYPE 7: Circular Ranking (less common in CUET/CLAT/IPMAT)
Key Rule:
No left/right concept; count clockwise or anticlockwise
consistently.
Example:
In a circular table A sits 4th to the left of B
→ Equivalent to B sitting 4th to the right of A.
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TYPE 8: Complex Multi-Statement Order & Ranking
Example (Moderate – IPMAT style):
Five students — A, B, C, D, E
Heights are different.
- A is
taller than B
- C is
shorter than D
- E is
taller than A
- C is
shorter than A
Arrange from tallest → shortest.
Solution:
From statements:
E > A > B
D > C
A > C
Combine:
E > A > D > C > B
Final answer:
E, A, D, C, B
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PYQs / PYQ-STYLE QUESTIONS with SOLUTIONS
(Based on CUET, CLAT, IPMAT pattern)
==========================================================
PYQ 1 (CUET-style)
In a class A is 18th from left and 25th from right. Find the
total number of students.
Solution:
Total = 18 + 25 – 1 = 42
PYQ 2 (CLAT-style)
In a row of students, Rina is 12th from the left and 18th
from the right. How many students are there?
Total = 12 + 18 – 1 = 29
PYQ 3 (IPMAT-style)
In a row of 50 students, A’s left rank is 14. B is 20 ranks
ahead of A. Find B’s left rank.
B = 14 – 20 = –6 → Not possible
→ means B is ahead on the right side.
So B’s right rank = 20 – 14 + 1 = 7
Left rank = 50 – 7 + 1 = 44
PYQ 4 (CUET)
In a row of 40, R is 12th from left. S is 19th from right. 6
people sit between them. Find the total.
Total = 12 + 19 + 6 – 1 = 36
But total given = 40 → mismatch
→ They face opposite directions (indirect cue)
Correct formula:
Persons between = Total – (12 + 19)
= 40 – 31 = 9
PYQ 5 (Moderate – IPMAT)
A is 7th from top in a class of 60.
How many are below him?
Below = 60 – 7 = 53
MCQ 1.
In a row of students, A is 7th from the left. If the total
number of students is 25, what is A’s rank from the right?
a) 18
b) 19
c) 17
d) 20
Answer: b) 19
Explanation:
Right Rank = 25 – 7 + 1 = 19
MCQ 2.
Rita is 12th from the right and 17th from the left. How many
students are there?
a) 28
b) 29
c) 30
d) 31
Answer: b) 28
Explanation:
Total = 17 + 12 – 1 = 28
MCQ 3.
Seema is 15th from left. Her rank from right is 22. Total
students?
a) 36
b) 37
c) 35
d) 38
Answer: c) 36
Explanation:
15 + 22 – 1 = 36
MCQ 4.
A is 10th from the left and B is 14th from the left. How
many students are between them?
a) 3
b) 4
c) 5
d) 6
Answer: c) 3
Explanation:
Between = |14 – 10| – 1 = 3
MCQ 5.
In a row of 40, A is 14th from left. How many are to the
right of A?
a) 25
b) 26
c) 27
d) 28
Answer: c) 27
Explanation:
Right = 40 – 14 = 26, but excluding A → 27
MCQ 6.
A is 10th from right in a class of 50. What is his rank from
the left?
a) 39
b) 40
c) 41
d) 42
Answer: c) 41
Explanation:
Left = 50 – 10 + 1 = 41
MCQ 7.
In a line, A is 6th from left, B is 10th from right, and 4
are between them. Total students?
a) 21
b) 19
c) 20
d) 18
Answer: a) 19
Explanation:
Total = 6 + 10 + 4 – 1 = 19
MCQ 8.
A is 8th from left, B is 12th from left. How many students
are between them?
a) 2
b) 3
c) 4
d) 5
Answer: b) 3
Explanation:
12 – 8 – 1 = 3
MCQ 9.
In a row of 45, John is 9th from right. Rank from left?
a) 37
b) 36
c) 38
d) 39
Answer: a) 37
Explanation:
45 – 9 + 1 = 37
MCQ 10.
A is 14th from top in class of 80. How many are below?
a) 64
b) 66
c) 67
d) 65
Answer: d) 66
Explanation:
80 – 14 = 66
MCQ 11.
Ritu is 18th from the left and 23rd from the right. Total
students?
a) 40
b) 41
c) 42
d) 43
Answer: b) 40
Explanation:
18 + 23 – 1 = 40
MCQ 12.
In a row of boys, A is 6th from left. Only 9 boys are to his
right. How many boys total?
a) 14
b) 15
c) 16
d) 17
Answer: b) 16
Explanation:
Total = 6 + 9 = 15, including A → 16
MCQ 13.
A’s left rank is 15 and right rank is 19. Find total.
a) 32
b) 33
c) 34
d) 35
Answer: a) 33
Explanation:
15 + 19 – 1 = 33
MCQ 14.
A is 5th from left. B is 12th from right. Total 20 students.
How many between A & B?
a) 2
b) 3
c) 4
d) 5
Answer: d) 4
Explanation:
Left rank of B = 20 – 12 + 1 = 9
Between = 9 – 5 – 1 = 3
MCQ 15.
In a exam rankings, A is 13th from top. 7 students are below
B. Total = 40. If B is 4 ranks above A, what is B’s rank?
a) 8
b) 9
c) 10
d) 11
Answer: a) 9
Explanation:
B = A – 4 = 13 – 4 = 9
MCQ 16.
In a row, R is 9th from left. S is 17th from left. How many
between them?
a) 6
b) 7
c) 8
d) 9
Answer: b) 7
Explanation:
17 – 9 – 1 = 7
MCQ 17.
A is 11th from right in a row of 60. What is left rank?
a) 49
b) 50
c) 51
d) 52
Answer: c) 50
Explanation:
60 – 11 + 1 = 50
MCQ 18.
A is 18th from top and 25th from bottom. Total?
a) 41
b) 42
c) 43
d) 44
Answer: c) 42
Explanation:
18 + 25 – 1 = 42
MCQ 19.
A is 6th from left. If 3 students join to left of A, new
rank?
a) 7
b) 8
c) 9
d) 10
Answer: c) 9
Explanation:
6 + 3 = 9
MCQ 20.
A is 12th from right in 100. How many are to left?
a) 87
b) 88
c) 89
d) 90
Answer: b) 89
Explanation:
Left = 100 – 12 = 88, excluding A = 87, but left count asked =
88.
MCQ 21.
Two students are between A (5th) and B (8th). How many
total?
a) 8
b) 9
c) 10
d) 11
Answer: a) 8
Explanation:
Positions possible = 5, x, x, 8 → total = 8
MCQ 22.
In a row of 75, rank of A from left is 25. How many to
right?
a) 50
b) 49
c) 48
d) 51
Answer: b) 50
Explanation:
75 – 25 = 50
MCQ 23.
In a class of 90, Sam is 30th from bottom. From top?
a) 59
b) 60
c) 61
d) 62
Answer: b) 61
Explanation:
Top = 90 – 30 + 1 = 61
MCQ 24.
Rohan is 14th from left, 15th from right. Total?
a) 28
b) 29
c) 30
d) 31
Answer: a) 28
Explanation:
14 + 15 – 1 = 28
MCQ 25.
In a row, A is 9th from left. If 2 boys to left leave, rank
becomes?
a) 6
b) 7
c) 8
d) 9
Answer: b) 7
Explanation:
9 – 2 = 7
MCQ 26.
A is 15th from right. Total is 35. Find left rank.
a) 19
b) 20
c) 21
d) 22
Answer: c) 21
Explanation:
Left = 35 – 15 + 1 = 21
MCQ 27.
In a row, A is 5th, B is 12th. 3 persons between. Check
correctness.
a) Possible
b) Not possible
Answer: a) Possible
Explanation:
12 – 5 – 1 = 6 ≠ 3 → Only possible if directions differ.
MCQ 28.
Total = 50, A is 20th from left. B is 15th from right.
Between them?
a) 13
b) 14
c) 15
d) 16
Answer: a) 14
Explanation:
Left rank of B = 50 – 15 + 1 = 36
Between = 36 – 20 – 1 = 15
MCQ 29.
In a queue, A is 8th from front, 12 from back. Total?
a) 18
b) 19
c) 20
d) 21
Answer: b) 19
Explanation:
8 + 12 – 1 = 19
MCQ 30.
If A is 14th from top in 60. What is his bottom rank?
a) 46
b) 47
c) 48
d) 49
Answer: b) 47
Explanation:
60 – 14 + 1 = 47
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