5th Class Mental Ability Ranking and Ordering-Test Order and Ranking

Order and Ranking

Category : 5th Class

 

                                                               Order and Ranking

 

Learning Objectives

  • To get aware of Ranking.
  • Increasing interest about this segment of reasoning.
  • Improving the general awareness.
  • Increasing the word power.

 

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.

 

  • Example:

 

3rd from left

3rd from right

Total \[=3+31\]

Same for vertical and Horizontal

  1. \[\text{Total+1=top+Bottom}\]
  2. \[Top=Total+1Bottom\]
  3. \[Bottom=Total+1Top\]
  4. \[\text{Total=Top+Bottom--1}\]

 

  1. In a row of 40 students, A is 13th from the left end, find the rank from right end.

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

  1. Total number of persons = {(sum of positions of same person from both sides i.e. left and right side) - 1}

OR

  1. Position of a person from opposite side = {(Total no. of persons - Position of same person from given side) +1}

 

  • Example:
  1. In a row of persons, position of A from left side of the row is 27th and position of A from right side of the row is 34th. Find total no. of persons in the row?

Explanation: Total no. of students = (Position of A from left + Position of A from right) -1

\[\Rightarrow \] Total no. of students \[=\left( 27+34 \right)-1=61-1=60\]

 

  1. In a row of 16 persons, position of A from left side of the row is 12th. Find the position of A from right side of the row?

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

  1. Total no. of persons = No. of persons after or before the given person in a row + Position of same person from the other side

OR

  1. No. of persons after or before the given person in a row = Total no, of persons - Position of same person from other side

 

  • Example:
  1. In a row of persons, position of A from left side of the row is 27th and there are 5 persons in the row after A. Find total no. of persons in the row.

Explanation: No. of persons in the row = Position of A from left + No. of persons after A.

\[\Rightarrow \] Total no. of persons \[=27+5=32\]

 

  1. In a row of 18 persons, position of A from left side of the row is 6th. Find the no. of persons in the row after A.

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-

  1. When there is no overlapping: i.e. the sum of position of the two persons from opposite ends < total number of persons
  2. When there is overlapping i.e. the sum of position of the two persons from opposite ends > total number of persons

 

Case - I

No. of students between two different persons = Total no. of students - (Sum of position of two different persons from opposite sides)

 

  1. In a row of 54 persons, A is 15th from the left side of the row and B is 20th from the right side of the row. Find the no. of persons sitting between A and B?

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

 

  1. In a row of 54 persons, A is 35th from the left side of the row and B is 22nd from the right side of the row. Find the no. of persons sitting between A and B.

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.

 

  • Example:
  1. In a row, position of A from left side of the row is 18th and position of B from right side of the row is 25th. Find the total no, of students in the row.

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.

  • Position of 2nd person from the same side as before interchanging = Position of 2nd person from same side before interchanging + (Position of 1st person after interchanging - position of 1st person before interchanging from same side)
  • To find total no. of students, find the person whose position from both sides can be depicted from the statement. Add both his positions from opposite ends and subtract 1.
  • To find no. of persons between them, difference in the position of common person whose position from same side before and after interchanging is given then subtract 1

 

  • Example:
  1. A and B are standing in a row of persons. A is 18th from left side of the row and B is 24th from right side of the row. If they interchange their positions, A becomes 31st from left. Find-

(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

 

  • Example:
  1. In a row of persons, position of A from left side of the row is 9th & position of B from right side of the row is 8th. If C is sitting just in the middle of A & B and position of C from left side of the row is 15th. Find the total no. of persons in the row?

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 \[=\left( 15+14 \right)-1=29-1=28\]

 

  1. In a row of persons. Position of A from left side of the row is 11th and B from right side of the row is 19th. If C is sitting just in the middle of A & B and position of C from A is 7th. Find total no. of persons in the row?

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

 

  • Example:
  1. If position of A from left side of a row is 15th and position of B from right side of a row is 19th and only 1 person is sitting in middle of A & Be Find the minimum number of persons that can be seated in this row.

Explanation: Total no. of persons \[=15+19-1-2=31\]

 

Commonly Asked Question

  1. In a group of 40 girls, when Karina was shifted by 4 places towards her right, then she became llth from the left end. What was her earlier position from the right end of the row?

(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-

  1. Aloke ranked higher than Suresh.
  2. Suresh ranked higher than Prakash.
  3. Aloke ranked lower than Nikhil.
  4. Kabir ranked between Aloke and Suresh,

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:

  1. Family
  2. Community
  3. Member
  4. Locality
  5. Country

(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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