Order & Ranking • Arrangements in ascending/descending order • Position-based questions
Order & Ranking: Full-Length Notes
Topics Covered:
Arrangements in Ascending/Descending Order
Position-Based Questions
1. Introduction to Order & Ranking
Order and Ranking is a key topic in logical reasoning and aptitude tests. It involves determining the position or rank of individuals or objects in a sequence based on given information. This topic tests your analytical thinking, attention to detail, and ability to handle indirect information.
2. Basic Concepts
Order: Arrangement of items or persons in a sequence (either ascending or descending).
Ranking: Assigning a position to each item/person in the sequence.
Total Number Calculation: Sometimes, you need to find the total number of items/persons based on positions from both ends.
3. Arrangements in Ascending/Descending Order
A. Ascending Order
Arranged from smallest to largest (e.g., height, age, marks).
Example: If five students are arranged in ascending order of marks, the one with the least marks is first, and the one with the highest is last.
B. Descending Order
Arranged from largest to smallest.
Example: If five students are arranged in descending order of height, the tallest is first, and the shortest is last.
C. Example Problems
Example 1:
Five students scored 45, 67, 89, 34, and 56 marks. Arrange them in ascending order.
Answer: 34, 45, 56, 67, 89
Example 2:
Arrange the numbers 12, 5, 23, 8 in descending order.
Answer: 23, 12, 8, 5
4. Position-Based Questions
These questions involve finding the position of a person/object from either end of a row or in a group.
A. Types of Position-Based Questions
Finding Position from Opposite Ends
Finding Total Number
Finding Number of Persons Between Two
Interchanging Positions
Finding Rank after Exclusions/Inclusions
B. Standard Formulas
Total Number of Persons = (Position from Left) + (Position from Right) - 1
Example: If Ravi is 7th from the left and 4th from the right, total persons = 7 + 4 - 1 = 10
Number of Persons Between Two = (Position of 1st from one end) + (Position of 2nd from opposite end) - Total Number - 1
Example: If A is 5th from left, B is 7th from right in a row of 15, persons between A and B = 5 + 7 - 15 - 1 = -4 (If negative, they overlap or positions are impossible.)
C. Example Problems
Example 1:
In a row of 20 students, Ramesh is 7th from the left. What is his position from the right?
Answer: 20 - 7 + 1 = 14th from the right
Example 2:
In a row, John is 12th from the left and 9th from the right. How many students are there in the row?
Answer: 12 + 9 - 1 = 20
Example 3:
In a row of 30 students, A is 12th from the left and B is 17th from the right. How many students are between A and B?
Answer: 30 - (12 + 17) = 1 (So, 1 student between A and B)
Example 4:
In a row, if the position of a student is the same from both ends and there are 21 students, what is his position?
Answer: (21 + 1) / 2 = 11th from both ends
5. Tricks and Tips
Draw diagrams for complex arrangements.
Double-check positions: Left and right ends can be confusing.
Remember formulas for quick calculations.
If positions overlap or negative values occur, recheck the logic or arrangement.
6. Practice Examples
Ascending/Descending Order
Arrange 14, 9, 21, 3, 18 in ascending order.
Answer: 3, 9, 14, 18, 21
Arrange 45, 67, 23, 89 in descending order.
Answer: 89, 67, 45, 23
Position-Based
In a row of 18 students, Sita is 5th from the left. What is her position from the right?
Answer: 18 - 5 + 1 = 14th from the right
If John is 8th from the left and 13th from the right in a row, how many students are there?
Answer: 8 + 13 - 1 = 20
In a row of 25 students, A is 10th from the left and B is 12th from the right. How many students are between A and B?
Answer: 25 - (10 + 12) = 3
7. Common Question Types
Who is in the middle?
Who is at the extreme ends?
How many are between X and Y?
What is the rank of X from the right if from the left it is Y?
If two persons interchange positions, what is the new arrangement?
8. Conclusion
Order and Ranking problems require careful reading, logical arrangement, and sometimes use of simple formulas. Practice is key—draw diagrams, use formulas, and double-check your answers for accuracy.
Order & Ranking Practice Questions with Explanations
1. In a row of 25 students, A is 10th from the left. What is A’s position from the right?
Solution:
Total students = 25
Position from right = 25 - 10 + 1 = 16th
2. In a class of 40, B is 12th from the top. What is B’s rank from the bottom?
Solution:
Rank from bottom = 40 - 12 + 1 = 29th
3. In a queue, Sabnam is 9th from the front while Prakash is 12th from the back. Pankaj is exactly in the middle of both. If there are 30 people in the queue, what is Pankaj’s position from the front?
Solution:
Sabnam: 9th from front
Prakash: 12th from back ⇒ 30 - 12 + 1 = 19th from front
Middle position = (9 + 19) / 2 = 14th from front (since there are 10 positions between 9th and 19th, so 5 ahead of 9th is 14th)
Answer: 14th
4. In a row of 26 persons facing North, Person A is 13th from the right. After shifting him third to the left, what is his position from the left now?
Solution:
Position from right = 13th
Position from left = 26 - 13 + 1 = 14th
After shifting 3 to the left: 14 + 3 = 17th from left
5. In a row of 50 students, C is 15th from the left and D is 20th from the right. How many students are there between C and D?
Solution:
C from left = 15
D from right = 20
D from left = 50 - 20 + 1 = 31
Number between = 31 - 15 - 1 = 15
6. In a class, Rajesh is 15th from the top and Prakash is 25th from the bottom. Gyan is 10 places ahead of Prakash. If there are 10 students exactly between Rajesh and Gyan, how many students are there in the class?
Solution:
Prakash from bottom = 25
Gyan is 10 ahead ⇒ Gyan from bottom = 25 + 10 = 35
Gyan from top = Total - 35 + 1
Let total be N.
Rajesh from top = 15
Number between Rajesh and Gyan = (Gyan from top) - (Rajesh from top) - 1 = 10
So, Gyan from top = 15 + 10 + 1 = 26
N - 35 + 1 = 26 ⇒ N = 26 + 35 - 1 = 60
7. In a row of 80 persons, Deepak is 42nd from the left. What is his position from the right?
Solution:
Position from right = 80 - 42 + 1 = 39th
8. In a class of 75, Stuti is 13th from the top and Barkha is 25th from the bottom. How many participants are between Stuti and Barkha?
Solution:
Barkha from top = 75 - 25 + 1 = 51
Between = 51 - 13 - 1 = 37
9. In a row of 30, S is 8th from the left and T is 12th from the right. How many students are between S and T?
Solution:
T from left = 30 - 12 + 1 = 19
Between = 19 - 8 - 1 = 10
10. In a row of 20, A is 7th from the left. What is his position from the right?
Solution:
Position from right = 20 - 7 + 1 = 14th
11. In a row of 18, B is 5th from the left. What is her position from the right?
Solution:
Position from right = 18 - 5 + 1 = 14th
12. In a row of 15, C is 4th from the right. What is her position from the left?
Solution:
Position from left = 15 - 4 + 1 = 12th
13. In a row, John is 12th from the left and 9th from the right. How many students are there in the row?
Solution:
Total = 12 + 9 - 1 = 20
14. In a row of 30, A is 12th from the left and B is 17th from the right. How many students are between A and B?
Solution:
B from left = 30 - 17 + 1 = 14
Between = 14 - 12 - 1 = 1
15. In a row of 20, if the position of a student is the same from both ends, what is his position?
Solution:
Let position = x
x = 20 - x + 1
2x = 21 ⇒ x = 10.5
Since position must be integer, possible only if odd number of students. For 21 students: x = 11
But for 20, such a position does not exist.
16. In a row of 50, X is 20th from the left and Y is 15th from the right. How many students are between X and Y?
Solution:
Y from left = 50 - 15 + 1 = 36
Between = 36 - 20 - 1 = 15
17. In a row of 35, P is 8th from the left and Q is 10th from the right. How many students are between P and Q?
Solution:
Q from left = 35 - 10 + 1 = 26
Between = 26 - 8 - 1 = 17
18. In a row, A is 5th from the left and B is 7th from the right. If there are 15 students, how many are between A and B?
Solution:
B from left = 15 - 7 + 1 = 9
Between = 9 - 5 - 1 = 3
19. In a class, Anuj is ranked 9th from the top and 38th from the bottom. What is the total strength of the class?
Solution:
Total = 9 + 38 - 1 = 46
20. In a row, Vivek is 9th from the front and Sunil is 7th from the back. There are 6 students between them. What is the total number of students in the row?
Solution:
Total = 9 + 6 + 7 = 22
21. In a row, Sunaina is on the 16th floor from the bottom of a 28-floor building. What is her position from the top?
Solution:
Position from top = 28 - 16 + 1 = 13th
22. In a row of 78 soldiers, Ram is 25th from the left and Shyam is 20th from the right. How many soldiers are between them?
Solution:
Shyam from left = 78 - 20 + 1 = 59
Between = 59 - 25 - 1 = 33
23. In a row, Priya is 15th from the left and Garima is 19th from the right. They interchange positions, and Ram who sits 24th from the left sits at the 5th place to the left of Priya's new position. How many people are there in the row?
Solution:
After interchange, Priya is 19th from right = 24th from left (since total = 24 + 19 - 1 = 42)
Ram is 5th to the left of Priya's new position = 24 - 5 = 19th from left
So, total = 24 + 19 - 1 = 42
24. In a class, Aprajita’s rank from the top is 23rd and from the bottom is 15th. How many students are there in the class?
Solution:
Total = 23 + 15 - 1 = 37
25. In a row of 31 students, Raj is 8th from the left and Sita is 10th from the right. How many students are between Raj and Sita?
Solution:
Sita from left = 31 - 10 + 1 = 22
Between = 22 - 8 - 1 = 13
26. In a row, A is 6th from the left and B is 7th from the right. If there are 16 students, how many are between A and B?
Solution:
B from left = 16 - 7 + 1 = 10
Between = 10 - 6 - 1 = 3
27. In a class of 50, if a student is 15th from the top, what is his rank from the bottom?
Solution:
Rank from bottom = 50 - 15 + 1 = 36th
28. In a row of 40, if A is 10th from the left and B is 12th from the right, how many students are there between A and B?
Solution:
B from left = 40 - 12 + 1 = 29
Between = 29 - 10 - 1 = 18
29. In a class, Ramesh is 18th from the top and 23rd from the bottom. How many students are there?
Solution:
Total = 18 + 23 - 1 = 40
30. In a row of 60, if X is 25th from the left, what is his position from the right?
Solution:
Position from right = 60 - 25 + 1 = 36th
31. In a row of 45, Y is 15th from the left and Z is 20th from the right. How many students are between Y and Z?
Solution:
Z from left = 45 - 20 + 1 = 26
Between = 26 - 15 - 1 = 10
32. In a class of 35, if a student is 9th from the top, what is his position from the bottom?
Solution:
Position from bottom = 35 - 9 + 1 = 27th
33. In a row, A is 7th from the left and B is 11th from the right. If there are 20 students, how many are between A and B?
Solution:
B from left = 20 - 11 + 1 = 10
Between = 10 - 7 - 1 = 2
34. In a class, Priya is 5th from the top and 30th from the bottom. How many students are there?
Solution:
Total = 5 + 30 - 1 = 34
35. In a row of 50, A is 20th from the left and B is 15th from the right. How many students are between A and B?
Solution:
B from left = 50 - 15 + 1 = 36
Between = 36 - 20 - 1 = 15
36. In a row, X is 12th from the left and Y is 17th from the right. If there are 30 students, how many are between X and Y?
Solution:
Y from left = 30 - 17 + 1 = 14
Between = 14 - 12 - 1 = 1
37. In a class of 40, if a student is 21st from the top, what is his position from the bottom?
Solution:
Position from bottom = 40 - 21 + 1 = 20th
38. In a row of 28, A is 9th from the left and B is 13th from the right. How many students are between A and B?
Solution:
B from left = 28 - 13 + 1 = 16
Between = 16 - 9 - 1 = 6
39. In a row, Sita is 6th from the left and Rita is 8th from the right. If there are 20 students, how many are between Sita and Rita?
Solution:
Rita from left = 20 - 8 + 1 = 13
Between = 13 - 6 - 1 = 6
40. In a class, Aman is 15th from the top and 25th from the bottom. How many students are there?
Solution:
Total = 15 + 25 - 1 = 39
41. In a row, X is 11th from the left and Y is 14th from the right. If there are 30 students, how many are between X and Y?
Solution:
Y from left = 30 - 14 + 1 = 17
Between = 17 - 11 - 1 = 5
42. In a class of 50, if a student is 18th from the top, what is his position from the bottom?
Solution:
Position from bottom = 50 - 18 + 1 = 33rd
43. In a row of 35, A is 8th from the left and B is 10th from the right. How many students are between A and B?
Solution:
B from left = 35 - 10 + 1 = 26
Between = 26 - 8 - 1 = 17
44. In a row, A is 6th from the left and B is 7th from the right. If there are 16 students, how many are between A and B?
Solution:
B from left = 16 - 7 + 1 = 10
Between = 10 - 6 - 1 = 3
45. In a class of 50, if a student is 15th from the top, what is his rank from the bottom?
Solution:
Rank from bottom = 50 - 15 + 1 = 36th
46. In a row of 40, if A is 10th from the left and B is 12th from the right, how many students are there between A and B?
Solution:
B from left = 40 - 12 + 1 = 29
Between = 29 - 10 - 1 = 18
47. In a class, Ramesh is 18th from the top and 23rd from the bottom. How many students are there?
Solution:
Total = 18 + 23 - 1 = 40
48. In a row of 60, if X is 25th from the left, what is his position from the right?
Solution:
Position from right = 60 - 25 + 1 = 36th
49. In a row of 45, Y is 15th from the left and Z is 20th from the right. How many students are between Y and Z?
Solution:
Z from left = 45 - 20 + 1 = 26
Between = 26 - 15 - 1 = 10
50. In a class of 35, if a student is 9th from the top, what is his position from the bottom?
Solution:
Position from bottom = 35 - 9 + 1 = 27th
51. Arrange the numbers 12, 5, 23, 8 in ascending order.
Solution:
5, 8, 12, 23
52. Arrange 45, 67, 23, 89 in descending order.
Solution:
89, 67, 45, 23
53. Arrange 14, 9, 21, 3, 18 in ascending order.
Solution:
3, 9, 14, 18, 21
54. Arrange 34, 67, 12, 90, 56 in descending order.
Solution:
90, 67, 56, 34, 12
55. Arrange 11, 22, 33, 44, 55 in ascending order.
Solution:
11, 22, 33, 44, 55
56. Arrange 100, 99, 98, 97 in descending order.
Solution:
100, 99, 98, 97
57. Arrange 1.2, 2.3, 0.9, 3.4 in ascending order.
Solution:
0.9, 1.2, 2.3, 3.4
58. Arrange 76, 54, 89, 32, 65 in descending order.
Solution:
89, 76, 65, 54, 32
59. Arrange 23, 45, 67, 89, 12 in ascending order.
Solution:
12, 23, 45, 67, 89
60. Arrange 15, 25, 35, 45, 55 in descending order.
Solution:
55, 45, 35, 25, 15
61. In a row of 20 students, A is 5th from the left. What is his position from the right?
Solution:
20 - 5 + 1 = 16th
62. In a row of 16, B is 4th from the right. What is his position from the left?
Solution:
16 - 4 + 1 = 13th
63. In a row of 25, C is 10th from the left and D is 15th from the right. How many students are between C and D?
Solution:
D from left = 25 - 15 + 1 = 11
Between = 11 - 10 - 1 = 0
64. In a row of 17, E is 6th from the left. What is his position from the right?
Solution:
17 - 6 + 1 = 12th
65. In a row of 21, F is 8th from the left and G is 9th from the right. How many students are between F and G?
Solution:
G from left = 21 - 9 + 1 = 13
Between = 13 - 8 - 1 = 4
66. In a row of 18, H is 7th from the left. What is his position from the right?
Solution:
18 - 7 + 1 = 12th
67. In a row of 22, I is 5th from the right. What is his position from the left?
Solution:
22 - 5 + 1 = 18th
68. In a row of 19, J is 8th from the left and K is 6th from the right. How many students are between J and K?
Solution:
K from left = 19 - 6 + 1 = 14
Between = 14 - 8 - 1 = 5
69. In a row of 24, L is 9th from the left. What is his position from the right?
Solution:
24 - 9 + 1 = 16th
70. In a row of 28, M is 12th from the left and N is 10th from the right. How many students are between M and N?
Solution:
N from left = 28 - 10 + 1 = 19
Between = 19 - 12 - 1 = 6
71. In a row of 14, O is 3rd from the left. What is his position from the right?
Solution:
14 - 3 + 1 = 12th
72. In a row of 23, P is 8th from the left and Q is 12th from the right. How many students are between P and Q?
Solution:
Q from left = 23 - 12 + 1 = 12
Between = 12 - 8 - 1 = 3
73. In a row of 27, R is 11th from the left. What is his position from the right?
Solution:
27 - 11 + 1 = 17th
74. In a row of 13, S is 5th from the right. What is his position from the left?
Solution:
13 - 5 + 1 = 9th
75. In a row of 16, T is 4th from the left and U is 7th from the right. How many students are between T and U?
Solution:
U from left = 16 - 7 + 1 = 10
Between = 10 - 4 - 1 = 5
76. In a row of 22, V is 9th from the left. What is his position from the right?
Solution:
22 - 9 + 1 = 14th
77. In a row of 18, W is 6th from the left and X is 8th from the right. How many students are between W and X?
Solution:
X from left = 18 - 8 + 1 = 11
Between = 11 - 6 - 1 = 4
78. In a row of 20, Y is 7th from the right. What is his position from the left?
Solution:
20 - 7 + 1 = 14th
79. In a row of 25, Z is 9th from the left and A1 is 10th from the right. How many students are between Z and A1?
Solution:
A1 from left = 25 - 10 + 1 = 16
Between = 16 - 9 - 1 = 6
80. In a row of 21, B1 is 8th from the left. What is his position from the right?
Solution:
21 - 8 + 1 = 14th
81. In a row of 15, C1 is 4th from the right. What is his position from the left?
Solution:
15 - 4 + 1 = 12th
82. In a row of 17, D1 is 6th from the left and E1 is 7th from the right. How many students are between D1 and E1?
Solution:
E1 from left = 17 - 7 + 1 = 11
Between = 11 - 6 - 1 = 4
83. In a row of 24, F1 is 9th from the left. What is his position from the right?
Solution:
24 - 9 + 1 = 16th
84. In a row of 28, G1 is 12th from the left and H1 is 10th from the right. How many students are between G1 and H1?
Solution:
H1 from left = 28 - 10 + 1 = 19
Between = 19 - 12 - 1 = 6
85. In a row of 14, I1 is 3rd from the left. What is his position from the right?
Solution:
14 - 3 + 1 = 12th
86. In a row of 23, J1 is 8th from the left and K1 is 12th from the right. How many students are between J1 and K1?
Solution:
K1 from left = 23 - 12 + 1 = 12
Between = 12 - 8 - 1 = 3
87. In a row of 27, L1 is 11th from the left. What is his position from the right?
Solution:
27 - 11 + 1 = 17th
88. In a row of 13, M1 is 5th from the right. What is his position from the left?
Solution:
13 - 5 + 1 = 9th
89. In a row of 16, N1 is 4th from the left and O1 is 7th from the right. How many students are between N1 and O1?
Solution:
O1 from left = 16 - 7 + 1 = 10
Between = 10 - 4 - 1 = 5
90. In a row of 22, P1 is 9th from the left. What is his position from the right?
Solution:
22 - 9 + 1 = 14th
91. In a row of 18, Q1 is 6th from the left and R1 is 8th from the right. How many students are between Q1 and R1?
Solution:
R1 from left = 18 - 8 + 1 = 11
Between = 11 - 6 - 1 = 4
92. In a row of 20, S1 is 7th from the right. What is his position from the left?
Solution:
20 - 7 + 1 = 14th
93. In a row of 25, T1 is 9th from the left and U1 is 10th from the right. How many students are between T1 and U1?
Solution:
U1 from left = 25 - 10 + 1 = 16
Between = 16 - 9 - 1 = 6
94. In a row of 21, V1 is 8th from the left. What is his position from the right?
Solution:
21 - 8 + 1 = 14th
95. In a row of 15, W1 is 4th from the right. What is his position from the left?
Solution:
15 - 4 + 1 = 12th
96. In a row of 17, X1 is 6th from the left and Y1 is 7th from the right. How many students are between X1 and Y1?
Solution:
Y1 from left = 17 - 7 + 1 = 11
Between = 11 - 6 - 1 = 4
97. In a row of 24, Z1 is 9th from the left. What is his position from the right?
Solution:
24 - 9 + 1 = 16th
98. In a row of 28, A2 is 12th from the left and B2 is 10th from the right. How many students are between A2 and B2?
Solution:
B2 from left = 28 - 10 + 1 = 19
Between = 19 - 12 - 1 = 6
99. In a row of 14, C2 is 3rd from the left. What is his position from the right?
Solution:
14 - 3 + 1 = 12th
100. In a row of 23, D2 is 8th from the left and E2 is 12th from the right. How many students are between D2 and E2?
Solution:
E2 from left = 23 - 12 + 1 = 12
Between = 12 - 8 - 1 = 3
Comments
Post a Comment