Reasoning Skills
Symmetric Relation II (Ranking puzzles)
shikha
October 2, 2015

In reasoning skills, “Ranking” is another puzzling subject that can blast your mind, leaving no clue behind how to solve the problem. Without knowing the formula or shortcut, you will not be able to understand how to proceed and what to get. So as to solve ranking based problems as fast as possible, let’s go into the depth….

# Ranking

In Ranking, the problem usually asked to find out the rank of a person while standing in a queue or an object placed in some sequence. Ranking can be categorized in two ways:

1. Row-wise Ranking: When an object or a person placed in a row. The possibility of placement is Left to Right or Right to left.
2. Column- wise Ranking: When an object or a person placed in a column. The possibility of placement is Top to Bottom or Bottom to Top.

## Row-Wise Ranking

In Row wise Ranking object can be ranked from Left to Right or Right to Left. In this case, the formula used to find the total number of objects/person or rank from left or rank from right is as below:

#### Problem 1:

In a class, the total number of students is 40. Joy, who always topped the exams, is sitting 14th from right. What is his rank from the left if students are sitting in a row?

#### Solution:

Step1: Check whether Students are sitting in a row or column.

Step2: In Row-wise Ranking the formula we have:

RL (Left) +RR (Right) – 1 = Total number of objects/person

Step3: See what is given: Joy is sitting 14th from right = RR (Right) = 14 Total number of students = 40

Step4: Putting in the formula:

RL (Left) +14 – 1 = 40

RL (Left) = 40- 13 =27

RL (Left) = 27

Conclusion: Joy is sitting 27th from the left.

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#### Problem 2:

In a queue, A is standing 6th from left and B is sitting 5thfrom right. Three more persons C, D, E is sitting exactly in between both of them. Find out the total persons standing in a queue?

#### Solution:

Step1:Students are standing in a queue.

Step2: In Row-wise Ranking the formula we have:

RL (Left) +RR (Right) – 1 = Total number of objects/person

Step3: See what is given:

A is 6th from left= RL (left) = 6

B is 5th from right= RR (Right) = 5

Three persons standing in between C, D, E

Step4: A is at 6th rank implies six persons are standing in a queue, including A, B is at the 5th rank implies five persons are standing in a queue, including B and three are standing in between, so it comes up the total

Total= 6+5+3= 14

Conclusion: Total persons standing in a queue = 14

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#### Problem 3:

Students are sitting in a row. A is sitting in unknown position. 6 students are sitting left to A and 7 are sitting right to A. Find out the total students sitting in a row?

#### Solution:

Step1: Students are sitting in a row.

Step2: In Row-wise Ranking the formula we have:

RL (Left) +RR (Right) – 1 = Total number of objects/person

Step3:  See what is given:

Six people are sitting left to A implies A is at 7th from left= RL (Left) =7th

Seven people are sitting right to A implies A is at 8th from right= RR (right) =8th

Step4: Putting in the formula:

RL (Left) +RR (Right) – 1 = Total number of objects/person

7 +8 – 1 = Total number of objects/person

Conclusion: Total number of persons sitting in a row = 14.

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## Column-Wise Ranking

In Column wise Ranking object can be ranked from Top to bottom or bottom to Top. In this case, the formula used to find the total number of objects/person or rank from the top or rank from the bottom is as below:

#### Problem 1:

Vijay ranks 5th from the top and 32nd from the bottom in a class. How many students are there in a class?

#### Solution:

Step1: Students are standing in a column.

Step2: In Column-wise Ranking the formula we have:

RT (Top) +RB (Bottom) – 1 = Total number of objects/person

Step3: See what is given:

Vijay’s position from top= RT (Top) = 5

Vijay’s position from Bottom= RB (Bottom) = 32

Step4:Putting in the formula:

RT (Top) +RB (Bottom) – 1 = Total number of objects/person

5 + 32 -1 = Total number of students

Conclusion: Total number of students in a class =36.

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#### Problem 2:

Ashish ranks 5th from the top in a class of 40. What is his rank from the bottom in a class?

#### Solution:

Step1: Students are sitting in a column.

Step2: In Column-wise Ranking the formula we have:

RT (Top) +RB (Bottom) – 1 = Total number of objects/person

Step3: See what is given:

Ashish position from top= RT (Top) = 5

Total number of students = 40

Step4: Putting in the formula:

RT (Top) +RB (Bottom) – 1 = Total number of objects/person

5 + RB (Bottom) – 1 = 40 RB (Bottom) = 36th

Conclusion: Ashish ranks 36th from the bottom.

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