Order and Ranking
Category : 5th 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) \[\text{Left+Right=Total+1}\]
(2) \[\text{Left=Total+1--Right}\]
(3) \[\text{Right=Total+1--left}\]
(4) \[\text{Total=left+Right--1}\]
Note: The above formulas are only for a single person's position.
3rd from left
3rd from right
Total \[=3+31\]
Same for vertical and Horizontal
Explanation: Total = 40
A's rank from right side \[\text{=Total+1--left}\]
\[=40+113\]
\[=27+1\]
\[=28\]
2. In a line of girls, if Kamla's position from the left is 15th and from the right her position is 17th, how many girls are there in the line?
Explanation: Total no. of girls = Kamla's position from the left + her position from the right - 1
\[=15+17-1=31\]
3. In a line of girls Nivedita's position from the left is 18th and Priti’s position from the right is 22nd. If there are 5 girls between them, what is the total number of girls in the line?
Explanation: In this question there are two possible positions.
Position I.
\[\therefore \]Total no. of girls \[=18+5+22=45\]
Position II.
\[\therefore \] Total no. of girls \[=22+18-\] (5 + Priti + Nivedita)
\[=22+18-7=33\]
4. In a line of girls, Juli's position from the left is 10th while Lalli's position from the right is 16th. When they interchange their positions, Juli’s position becomes 20th from the left, then what will be the position of Lalli from the right?
Explanation: Original position:
Since Juli's new position after interchange is 20th from the left.
\[\therefore \] Total no. of girls in the line \[=20+15=35\]
Hence, Lalli's position from the right \[=\left( 35-10 \right)+1={{26}^{th}}\]
Types of Order and Ranking
Type-1
OR
Explanation: Total no. of students = (Position of A from left + Position of A from right) -1
\[\Rightarrow \] Total no. of students \[=\left( 27+34 \right)-1=61-1=60\]
Explanation: Position of A from right side = {(Total no. of persons - Position of A from left side) + 1}
\[\Rightarrow \] Position of A from right side \[=\left( 16-12 \right)+1=4+1={{5}^{th}}\]
Type - 2
OR
Explanation: No. of persons in the row = Position of A from left + No. of persons after A.
\[\Rightarrow \] Total no. of persons \[=27+5=32\]
Explanation: No. of persons after A = Total no. of persons - Position of A from left
\[\Rightarrow \] No. of persons after A in the row \[=18-6=12\]
Type - 3
When the position of two persons are given from opposite ends and we know the total number of persons, then two cases arise, when trying to determine the number of persons between these two persons-
Case - I
No. of students between two different persons = Total no. of students - (Sum of position of two different persons from opposite sides)
Explanation: Here Sum of position of A & B from opposite ends \[=15+20=35<\] Total no. of persons
\[\therefore \] No. of persons between A & B = Total no. of students - (Position of A from left + Position of B from right)
\[\Rightarrow \]No. of persons between \[A\And B=54-\left( 15+20 \right)=54-35=19\]
Case - II
No. of students between two different persons = (Sum of position of two different persons from opposite sides) - Total no. of students - 2
Explanation: Here Sum of position of A & B from opposite ends \[=35+22=57>\] Total no. of persons
\[\therefore \] No. of persons between A & B = (Position of A from Left + Position of B from right) - Total no. of students - 2
\[\Rightarrow \] No. of persons between \[A\And B=\left( 35+22 \right)-54-2=57-54-2=1\]
Type - 4
If total no. of students is to be calculated and positions of different persons from any side are given then it is always a case of 'cannot be determined’ or 'data inadequate' or 'can't say'. This is because we do not know if there is overlapping or not.
Explanation: Cannot be determined as position of different persons is given from the same side.
Type - 5
Positions of two persons are given and their positions are interchanged and after interchanging, position of 1st person is given from same side as before interchanging.
(i) New position of B from right side
(ii) Total no. of persons
(iii) No. of persons between A & B
Explanation:
(i) New position of B from right side = Position of B from right side before interchanging + (Position of A from left side after interchanging - Position of A from left side before interchanging)
\[\Rightarrow \] New position of B from right side \[=24+\left( 31-18 \right)=24+13=37th\]
(ii) Total no. of persons = (A's position from right before interchanging + A's position from left before interchanging) - 1
\[\Rightarrow \] Total no. of persons = (B's position from right after interchanging + A's position from left before interchanging) - 1
\[\Rightarrow \] Total no. of persons \[=\left( 24+31 \right)-1=55-1=54\]
(iii) No. of persons between A & B = (Position of A from left after interchanging" Position of A from left before interchanging) - 1
\[\Rightarrow \] No. of persons between \[A\And B=\left( 31-18 \right)-1=13-1-12\]
Type - 6
If positions of two different persons are given from opposite sides of the row and a third person is sitting exactly in middle of the two and total no. of persons in the row is to be calculated as
(i) When position of third person sitting is given from either side of row
(ii) When position of third person is given from either of the two persons between whom he/she is sitting
Then find the position of the 3rd person from both sides of the row and hence find total no. of persons according to type 1
Explanation: Petition of C from left is 15th and A from left is 9th so there are \[\left( 15-9-1=5 \right)\] persons are sitting between A and C. As C is sitting in middle of A and B so there must also be 5 persons sitting between B and C.
Thus position of C from right = Position of B from right \[+5+1=8+6=14th\]
Total no. of students = (Sum of positions of C from both sides - 1)
\[\Rightarrow \] Total no. of students \[=\left( 15+14 \right)-1=29-1=28\]
Explanation: Position of C from Left = Position of A from left + Position of C from \[A=11+7=18th\]
Given, C is 7th from A and C is sitting in middle of A and B. Also C is at 7th position from B
Position of C from right = Position of B from right + Position of C from \[B=19+7=26th\]
Total no. of students = (Sum of position of C from both sides - 1)
\[\Rightarrow \] Total no. of students \[=\left( 18+26 \right)-1=44-1=43\]
Type - 7
In the questions where it is asked to find minimum no. of persons in a row then it is always a case of overlapping i.e. given positions of persons from either sides overlap each other.
Then
Minimum no. of persons = Sum of positions of persons from both sides - Persons between them - 2
Explanation: Total no. of persons \[=15+19-1-2=31\]
Commonly Asked Question
(a) 34 (b) 32
(c) 33 (d) 35
(e) None of these
Answer: (c)
Explanation:
2. In a group of 40 boys, Prem is 12th from the left end and Raj is 17th from the right end. If Radhay is placed exactly between them what is his right hand rank?
(a) 22 (b) 23
(c) 24 (d) 25
(e) None of these
Answer: (b)
Explanation:
Members in between
\[24-12-1=11\] Or \[29-17-1=11\]
Why we subtract 1 is because we do not want to consider the 29th rank, we want the nos. between 29 and 17.
Radhey's rank from right \[=17+5+1=23\].
3. Vikas is taller than Shyam but shorter than Umesh. Umesh is taller Rajat but shorter than Ganesh. If Shyam is taller than Rajat who is the shortest among all?
(a) Ganesh (b) Umesh
(c) Rajat (d) Vikas
(e) Shyam
Answer: (c)
Explanation: According to the decreasing heights they are as follows:
Ganesh > Umesh > Vikas > Shyam > Rajat
Thus, Rajat is the shortest among all.
4. Five boys participated in an education competition-
Who ranked the highest?
(a) Nikhil (b) Aloke
(c) Suresh (d) Kabir
(e) Prakash
Answer: (a)
Explanation: Arrangement in decreasing order of rank.
Nikhil, Aloke, Kabir, Suresh, Prakash.
Thus, Nikhil ranked the highest.
5. Arrange the following words in a meaningful order:
(a) 3, 1, 2, 4, 5 (b) 3, 1, 2, 5, 4
(c) 3, 1, 4, 2, 5 (d) 3, 1, 4, 5, 2
(e) None of these
Answer: (a)
Explanation: Member is a part of family. Family is a part of community.
Community lives in a locality is a part of country. Thus, the correct order is 3, 1, 2, 4, 5.
6. In a class of 39 students, 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) 14th (b) 15th
(c) 16th (d) 17th
(e) None of these
Answer: (c)
Explanation:
Ravi's rank from the start \[=39-\left( 17+7 \right)+1=16th\]
7. Aruna ranks 12th in a class of 46. What will be her rank from the last?
(a) 33 (b) 34
(c) 35 (d) 37
(e) None of these
Answer: (c)
Explanation: Aruna's rank from the last \[=\left( 46-12 \right)+1=35\]
Thus, Arun's rank from the last would be 35.
8. In a group of five girls, Kamini is second in height. Pooja is taller than Monika. Rupa is the tallest and Neelam is taller than Pooja. If they are arranged in ascending order of heights, who is at third position?
(a) Monika (b) Rupa
(c) Monika or Rupa (d) Neelam
(e) None of these
Answer: (d)
Explanation: On arranging in ascending order of heights. Monika < Pooja < Neelam < Kamini < Rupa.
Hence, Neelam is at third position.
9. If a is taller than b, c is taller than d and d is taller than b, who is the tallest?
(a) a (b) b
(c) c (d) Cannot be determined
(e) None of these
Answer: (d)
Explanation: a > b, c > d > b.
\[\therefore \] Who is the tallest cannot be found.
10. Amit and Sumit are twins. Richa is younger than Sumit. Richa is younger than Jyoti but elder than Saurabh. Sumit is younger than Jyoti. Who is the eldest of all?
(a) Amit (b) Jyoti
(c) Richa (d) Saurabh
(e) None of these
Answer: (b)
Explanation: Jyoti > Amit = Sumit > Richa > Saurabh.
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