Order and Ranking
Category : 4th Class
Order and Ranking
Learning Objectives
Introduction
Ranking is based on the arrangement of things in a particular order. The arrangement may be on the basis of their position, size, age etc.
Position Series Test
In this series, questions are asked about the positions of the persons from up or down, or from left or right, etc. Some important types are as given below
Order and Ranking Concepts:
Formulas to determine the positioning of a person:
(1) \[\text{Left}+\text{Right}=\text{Total}+1\]
(2) \[\text{Left}=\text{Total}+1-\text{Right}\]
(3) \[\text{Right}=\text{Total}+1-\text{Left}\]
(4) \[\text{Total}=\text{Left}+\text{Right}-1\]
Note: the above formulas are only for a single person's position.
Same is for vertical and horizontal positioning of a person.
(1) \[\text{Total}+1=\text{top}+\text{Bottom}\]
(2) \[\text{Top}=\text{Total}+1-\text{Bottom}\]
(3) \[\text{Bottom}=\text{Total}+1-\text{Top}\]
(4) \[\text{Total}=\text{Top}+\text{Bottom}-1\]
PART-II (Same Positions)
Example:
1. In a row of persons, position of Raj from left side of the row is 17th and position of Raj from right side of the row is 24th. Find total number of persons in the row.
Explanation:
Total number of persons = (Position of A from left + Position of A from right) -1
\[\Rightarrow \]Total number of persons = \[\left( 17+24 \right)-1=41-1=40\]
2. In a row of 12 persons, position of A from left side of the row is 8th. Find the position of A from right side of the row.
Explanation:
Position of A from right side = {(Total number of persons - Position of A from left side) +1}
\[\Rightarrow \]Position of A from right side = \[\left( 12-8 \right)+1=4+1=5\text{th}\] position.
Commonly Asked Question
1. In a row of persons, position of A from left side of the row is 13th and position of A from right side of the row is 31th. Find total number of persons in the row.
(a) 45 (b) 44
(c) 43 (d) 42
(e) None of these
Answer (c) is correct.
Explanation:
Total number of persons = (Position of A from left + Position of A from right) \[-1\]
\[\Rightarrow \]Total number of persons =\[\left( 13+31 \right)-1=44-1=43\].
Rest of the options is incorrect because of the correctness of option (c).
2. In a row of persons. Raj is 18th from left end and 41th from right end. Find out total number of persons in the row.
(a) 49 (b) 52
(c) 58 (d) 62
(e) None of these
Answer (c) is correct.
Explanation:
Total number of persons = (Position of A from left + Position of A from right) \[-1\]
\[\Rightarrow \]Total number of persons =\[\left( 18+41 \right)-1=59-1=58\].
Rest of the options is incorrect because of the correctness of option (c).
3. In a row of 40 persons, position of A from left side of the row is 12th. Find the position of A from right side of the row.
(a) 27 (b) 28
(c) 29 (d) 30
(e) None of these
Answer (c) is correct.
Explanation:
Position of A from right side = {(Total number of persons \[-\] Position of A from left side) +1}
\[\Rightarrow \]Position of A from right side =\[\left( 40-12 \right)+1=28+1=29\].
Rest of the options is incorrect because of the correctness of option (c).
4. In a class of 39, Ravi is 7 ranks ahead of Sumit. If Sumit’s rank is 17th from the last, what is Ravi's rank from the Start?
(a) 24 (b) 32
(c) 16 (d) 39
(e) None of these
Answer (c) is correct.
Explanation:
Total = \[\text{L}+\text{R}-1\]
\[\text{39=L}+24-1\]
\[\text{L}=39-23\]
\[\text{L}=16\].
Rest of the options is incorrect because of the correctness of option (c).
5. In a class Rakesh ranks 7th from the top and 28th from the bottom. How many students are there in the class?
(a) 34 (b) 42
(c) 26 (d) 25
(e) None of these
Answer (a) is correct.
Explanation:
Rakesh
Total number of students
= (Position of Rakesh from Top + Position of Rakesh from Bottom) \[-1\]
= \[(7+28)-1\]
= \[35-1=34\].
Rest of the options is incorrect because of the correctness of option (a).
PART-II (Interchanging Positions)
6. In a row of girls, Meena is 8th from the left and Reena is 17th from the right. If they interchange their positions, Meena becomes 14th from the left. How many girls are there in the row?
(a) 30 (b) 28
(c) 26 (d) 25
(e) None of these
Answer (a) is correct.
Explanation:
Since Meena and Reena interchange positions, so Meena's new position is the same as Reena's earlier position.
This position is 14th from the left (Meena's new position) and 17th from the right (Reena's earlier position).
Total = \[\text{L}+\text{R}-1\]
Total = \[14+17-1\]
Total = \[31-1=30\]
Hence, total number of girls in the row is 30.
Rest of the options is incorrect because of the correctness of option (a).
7. In a row of children, Reena is fifth from the left and Raj is sixth from the right. When they interchange their places among themselves, Reena becomes thirteenth from the left. Then what will be Raj's position from the right?
(a) 18 (b) 14
(c) 20 (d) 22
(e) None of these
Answer (b) is correct.
Explanation:
Since Reena and Raj interchange places, so Reena's new position (13th from left) is the same as Raj's earlier position (6th from right).
So, number of children in the queue =\[\left( 13+6 \right)-1=19-1=18\].
Now, Raj's new position is the same as Reena's earlier position fifth from left.
Therefore Raj's position from the right =\[\left( 18-5 \right)+1=14\text{th}\].
Rest of the options is incorrect because of the correctness of option (b).
8.
(a) 29 (b) 35
(c) 19 (d) 25
(e) None of these
Answer (a) is correct.
Explanation:
T = \[15+15-1=29\]
Rest of the options is incorrect because of the correctness of option (a).
9. In a class of 35 students, A is placed seventh from the bottom where as B is placed ninth from the top. C is placed exactly in between the two. What is A's position from C?
(a) 10th (b) 12th
(c) 15th (d) 29th
(e) None of these
Answer (a) is correct.
Explanation:
A’s position from C is = \[19-9=10\text{th}\]
Rest of the options is incorrect because of the correctness of option (a).
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