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**Order and Ranking**

For this topic, the questions are asked for a person related to its rank from **left/right/top/bottom side **is given to us and the total required persons are asked. While the opposite can also be asked in some cases.

Thus, many different types of questions can be formed based on position or the rank of the persons in the row.** There are many different types of cases which are asked from order and ranking. Here, below are the types of these cases:**

- Rank of a person from the right or left side
- Total number of people for the data which is given
- Maximum or minimum number of people in one row
- Total number of people between the two people
- After interchanging the position rank of a person.

**Case 1: Rank of a person from the right side or left side**

Here we are required to find the number of people who are in a row. The rank of two people and the total number of people sitting between two people is given to us. There are two cases possible in this scenario.

One is an overlapping case where a number of people > right position of one person + left position of another person. So, the total people = Sum of positions of two different people from both the sides + the no. of people between two people.

Example: There are 52 people in one row. Raj is the 14th person from the left side of this row. Rohan is a 10th person from the right side. How many people are sitting between these two?

So, the total number of people between Raj and Rohan is 52 – (14 + 10) = 18.

**Case 2: Overlapping case: Number of students < Right position of a person + Left position of another person)**

Example: There 46 people in a row. Raj is 26th person from the right side of the row. Rohan is a 32nd person from the left side of the row. Find out the total number of people sitting between these two.

So, total number of people = (26 + 32) – 46 – 2 = 58 – 44 = 14 people.

**Case 2: Total number of people for the data which is given**

So, here we have to determine the number of people when the ranks of a person are given from both the sides of the row.

Thus, Total persons are R1 + R2 – 1

R represents the ranks of a person from both sides.

Example: Position of Atul in a row is 26th from the right side of the row. He is sitting 38th from the left side of the row. Find out the total number of people in the row.

So, here the total people will be (position of Atul from the left side + the position of Atul from the right side) – 1.

Thus, total people = (38 + 26) – 1 = 63

**Case 3: Maximum or minimum number of people in one row**

In this scenario, the position of two persons are given and their positions are interchanged in a row. Here the interchanging the position for a 1st person is from the same side as that before the interchange.

So, a new position for the 2nd person from the side is the position of the 2nd person from the similar side before the interchange + (position of 1st after the interchange – position of 1st before interchange from the similar side).

Total people = Sum of the person from both the sides – 1. Total people between two persons = Difference in the people’s position who position from the similar side after and before the interchange is provided – 1.

**Example: Pramod is 13th from the left side and Kanak is 20th from the right side in a row. They decided to interchange their positions, now Pramod becomes 18th from the left side. What will Kanak’s position be from the right?**

Total girls given in the row = Right side + Left side – 1. This is 18 + 20 – 1 = 37. Kanak’s position from the right side = Total number of girls – Left end + 1 = 37 – 13 + 1 = 25

**Q1. There are five books of different weights. A is heavier than C and B is heavier than D. E is lighter than B but heavier than C. D is lighter than C. Which is the lightest book?**

**(a) E**

**(b) D**

**(c) B**

**(d) C**

S1. Ans. (b)

Sol. A is heavier than C and B is heavier than D

A > C and B > D

E is lighter than B but heavier than C. D is lighter than C.

B > E > C > D

Thus, we can definitely say from the above conditions that D is the lightest book.

**Q2. From a group of five friends, A is taller than B but not as tall as C, who is shorter than D. E is shorter than D but not shorter B. Who is the shortest among them?**

**(a) A**

**(b) E**

**(c) B**

**(d) None of these**

S2. Ans. (c)

Sol. A is taller than B but not as tall as C, who is shorter than D.

D > C > A > B

E is shorter than D but not shorter B.

D > E > B

Thus, we can definitely say from the above conditions that B is the shortest among all of them.

**Q3. Among States A, B, C, G, and E, State B is bigger than State C but smaller than State A, which is smaller than State E. State G is smaller than State E and not smaller than State A. How many states are better than State G?**

**(a) One**

**(b) Two**

**(c) Three**

**(d) None of these**

**S3. Ans. (a)**

Sol. State B is bigger than State C but smaller than State A, which is smaller than State E.

E > A > B > C

State G is smaller than State E and not smaller than State A.

E > G > A > B > C

Thus, we can say one state is better than State G.

**Q4. Rakesh obtained more marks than Suresh but less than Santosh. Ramesh obtained more than Rajesh but less than Harish. Santosh obtained less than Rajesh. Who obtained the highest marks?**

**(a) Santosh**

**(b) Rakesh**

**(c) Ramesh**

**(d) Harish**

**S4. Ans. (d)**

Sol. Rakesh obtained more marks than Suresh but less than Santosh.

Santosh > Rakesh > Suresh

Ramesh obtained more than Rajesh but less than Harish.

Harish > Ramesh > Rajesh

Santosh obtained less than Rajesh.

Harish > Ramesh > Rajesh > Santosh > Rakesh > Suresh

Thus, we can say Harish obtained the highest marks.

**Q5. In a group of five friends A, B, C, D, and E, B is younger to C but elder to A. If arranged in ascending order of age, then D gets the fifth rank and E is fourth, who is the youngest in age?**

**(a) B**

**(b) A**

**(c) Either E or C**

**(d) None of these**

S5. Ans. (b)

Sol. B is younger to C but elder to A.

C > B > A

D gets the fifth rank and E is fourth when arranged in ascending order wise.

D > E > __ > __ > __

Thus on combining the above conditions, we can definitely say D > E > C > B > A

And A is the youngest among the five friends.