**Order and RANKING**

In this chapter generally the ranks of a person from both sides left or right or from top and from bottom are mentioned and total numbers of persons are asked. In other words

a set, group or series of numerals is given and the candidates is asked to trace out numerals following certain given conditions. Sometimes the questions are based on their interchanged positions.

**There are mainly three/four types of questions -**

1. Total persons and position of one person (either from left or right) are given.

2. Position of more than one person is given.

3. Over lapping conditions:

**a. Overlapping case:**

**When (left + right) positions > Total number of students**

**b. Not overlapping case:**

**When Total number of students > (left +right) positions**

4. Ascending/Descending Order according age, height, marks etc.

**We have to find out:**

1. Position from other side.

2. Total number of persons.

3. Number of persons in between

4. Minimum/maximum number of persons in the row.

5. Number of persons on either side of a particular person.

**Formulas for Order and Ranking**

**· Finding ranks either from left or from right:**

Total – (given rank – 1) = required rank

**· Finding total numbers:**

When ranks of one person is given from both sides of the row.

Ranks of common person from both sides (R1 + R2) – 1

**· Finding total number of the person: (Misc. Case)**

When ranks of two persons and number of the persons who are sitting between these two persons are given.

(a) (R1+R2) + number of middle persons

(b) (R1+R2) - (number of middle persons +2)

**NOTE:**Apply condition (b) only for overlapping case.

**· Finding the number of persons who are sitting between any two persons: (Simple case)**

**Total -**

**(Rank from left + Rank from right)**

**· Finding the number of persons who are sitting between any two persons: (Overlapping Case)**

**(Rank from left + Rank from right) - (Total + 2)**

**· Finding Rank of middle person: (Quick Trick)**

Step 1- Convert both ranks from same side (side from which rank of exactly mid asked)

Step 2- Finds the average of both ranks (answer)

**· Shortcut for calculating total number of maximum and minimum persons in a row:**

**NOTE:**Mid no. means number of the middle persons.

**Examples: 1 Here is a table.**

Let discuss about ‘Ema’

Ema’s rank from top = 1 and from bottom = 5

Now total member in the row = 5

Means total rank = (rank from top + rank from bottom) – 1

= (1+ 5) – 1 = 5

Rank from top = total rank – (rank from bottom-1)

= 5 – (5-1) = 1

Rank from bottom = total rank – (rank from top – 1)

= 5 – (1-1) = 5

**Examples:2 Meenam is fourteenth from the right end in a row of 40 girls. What is her position from the left end?**

(1) 24th (2) 25th (3) 26th (4) 27th (5) None of these

**EXPLANATION:**

Clearly, number of girls towards the right of Meenam = 13

So, Meenam’s rank from left end = 40 – 13 = 27th

Ans. (4)

**Examples:3**

**Raju is seventh from left and Rohan is ninth from right.**

**If there are six students between them then how many students are there in a row?**

(1) 8 (2) 10 (3) 22 (4) 21 (5) Cannot be determined

**EXPLANATION:**

Total number of students in a row = 7+9+6 = 22

Ans (3)

**Note:**We cannot apply overlapping case in this question because if we are applying overlapping case then the minimum student is eight which conflict with the rank of Rohan from right.

**Examples:4 Rohan’s rank 25 from the top and Sohan’s rank 30 from the bottom. If there are three students in between Rohan and Sohan then find out the total number of student ?**

(1) 50 (2) 62 (3) 58 (4) Can't be determined (5) None of these

**EXPLANATION:**

Ans (4) Either (1) or (3) Minimum student = 50 while maximum student 58.

**Examples:5 Ram is eighth from left end and is fourth to the left of Shyam who is eighth from right end. Then how many students are there in a row?**

(1) 19 (2) 21 (3) 24 (4) 20 (5) None of these

**EXPLANATION:**

Total students in a row = 8 + 3 + 8 = 19

**Ans: (1)**

**Examples:6 In a row of boys facing towards North, A is sixteenth from the left end and C is sixteenth from the right end. B, who is fourth to the right of A, is fifth to the left of C then. How many boys are there in the row?**

(1) 39 (2) 40 (3) 41 (4) 42 (5) None of these

**EXPLANATION:**

Clearly, according to the given conditions, there are 15 boys to the left of A, as well as to the right of C. Also, B lies between A and C such that there are 3 boys between A and B; and 4 boys between B and C.

So, number of boys in the row = (15 + 1+ 3 + 1+4 +1+15)

= 40

Ans: (2)

**Examples:7 Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there are three persons ahead of C and 21 behind A, then what could be the minimum number of persons in the queue?**

(1) 27 (2) 28 (3) 40 (4) 41 (5) None of these

**EXPLANATION:**

As per the given conditions, there are two possible arrangements as shown below:

Clearly, for the minimum number of person, we shall consider arrangement (ii).

In (ii), number of persons in the queue

= (3 + 1 + 2 + 1 + 21) = 28.

**Ans. (2)**

**Examples:8 In a row of 40 girls, when Komal was shifted to her left by 4 places her number from the left end of the row became 10. What was the place of Swati from the right end of the row if Swati was three places to the right of Komal’s original position?**

(1) 22 (2) 23 (3) 25 (4) 26 (5) None of these

**EXPLANATION:**

On shifting 4 places to the left, Komal becomes 10th from the left end of the row. Thus, Komal’s original position was 14th from the left end.

Swati is 3 places to the right of Komal’s original position.

Clearly, Swati is 17th from the left end.

Number of girls to the right of Swati = (40 – 17) = 23.

Thus, Swati is 24th from the right end of the row.

**Ans. (5)**

**Examples:9 Study the following information carefully and answer the questions given below.**

**In a class of boys and girls, Jadeja's rank is 20th and Sunanda's rank is 11th.**

**Jadeja's rank among the boys is 11th and Sunanda's rank among the girls is 6th.**

**In the class, Sunanda's rank is 64th from the other end.**

**From the other end, Jadeja's rank among the boy's is 34th.**

**Q.1. How many total boys and girls in the class?**

(1) 65 (2) 77 (3) 71 (4) 74 (5) None of these

**Q.2. How many girls are there between Jadeja and last rank holder (assuming it is a boy) in the class?**

(1) 25 (2) 21 (3) 23 (4) 22 (5) None of these

**Explanations of Q-1 and Q-2:**

**Examples:10 Study the following information carefully and answer the questions given below-**

**Among Nikhil, Moon, Kapil, Jagdish and Gulshan each securing different marks in a subject, Moon secured more marks than only Kapil. Gulshan and Jagdish secured less marks than only Nikhil.**

**Q.1. Who among them secured third least marks?**

(1) Nikhil (2) Jagdish (3) Moon (4) Cannot be determined (5) None of these

**Q.2. If Nikhil secured 80 marks and Jagdish secured 65 marks then what is the possibility of Gulshan’s marks?**

(1) 78 (2) 63 (3) 60 (4) Cannot be determined (5) None of these

**Explanation:**

**Examples:11 Among Zojo, Yo, Xe, William and Vicky each scoring different marks in a test. Xe scored more than William but not as much as Vicky. Vicky scored more than Zojo, who scored less than Yo. Who did score second highest marks?**

(1) Yo (2) Zojo (3) Xe (4) Data inadequate (5) None of these

**Explanation:**

Ans: (4)

**Examples:12 Zombo, correctly remembers that his father's birthday is before 29th July but after 24th July whereas his younger brother correctly remembers that their father's birthday is after 23rd July but before 28th July and his elder brother correctly remembers that their father's birthday is on an odd date. On which date of July is definitely their father's birthday?**

(1) Twenty-five or Twenty-seven (2) Twenty-seven (3) Twenty-five (4) Twenty-six (5) None of these

**Explanation:**

Ans: (1)

**Examples:13 In the row of 40 students, Mahesh is 28th from left end and Suresh is 25th from right end. If Danish is sitting exactly in between them, what will be Danish’s position from left?**

(1) 14 (2) 22 (3) 28 (4) 18 (5) None of these

**Explanation:**

Ans: (2)

**Examples:14 Jai is 25th from left and Vijay is 24th from right. When they interchange their positions respectively then Vijay becomes 31st from right end. What will be Jai's position from left after interchanging?**

(1) 25 (2) 26 (3) 27 (4) 28 (5) None of these

**Explanation:**

Jai's position from the left after interchanging = 25 + 6 + 1 = 32

Ans: (5)

**Examples:15 In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, then Rita and Monika occupy seventeenth place from the right and eighteenth place from the left respectively. How many girls are there in the row?**

(1) 25 (2) 26 (3) 27 (4) Data inadequate(5) None of these

**Explanation:**

Ans: (2)

**Examples:16**

**Ram is 27th place from left end in the row of 44 boys. Rohit is 15th from the right end in the same row .How many boys are there between them in the row?**

(1) Eleven (2) Ten (3) Six (4) Two (5) None of these

**Explanation:**

Ans: (4)

**Examples:17**

**Students line up in a queue in which Aman stands fifteenth from the left and Simran is seventh from the right. If they interchange their places, Simran would be fifteenth from the right. How many students are there in the queue?**

(1) 21 (2) 22 (3) 28 (4) 29 (5) None of these

**Explanation:**

Simran’s new position is 15th from the right as well as the left end of the row.

Therefore number of students in the queue = (14 + 1 + 14) = 29.

Ans: (4)

**Examples:18**

**In a queue of children, Ajay is fifth from the left and Sunil is sixth from the right. When they interchange their places among themselves, Ajay becomes thirteenth from the left. Then, what will be Sunil's position from the right?**

(1) 8th (2) 14th (3) 15th (4) 16th (5) None of these

**Explanation:**

Since Ajay and Sunil interchange places, so Ajay’s new position (13th from left) is the same as Sunil’s earlier position (6th from right).

So, number of children in the queue = (12 + 1 + 5) = 18.

Now, Sunil’s new position is the same as Ajay's earlier position fifth from left.

Therefore Sunil’s position from the right = (18 - 4) = 14th.

Ans: (2)

**Examples:19**

**Kunal ranked sixteenth from the top and twenty ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?**

(1) 35 (2) 45 (3) 50 (4) 55 (5) None of these

**Explanation:**

Number of boys who passed = (15 + 1 + 28) = 44

Total number of boys in the class = 44 + 6 +5 = 55.

Ans:(4)

**Examples:20**

**In a queue, Vijay is fourteenth from the front and Jack is seventeenth from the end, while Mary is exactly at the middle of Vijay and Jack. If Vijay be ahead of Jack and there be 48 persons in the queue, how many persons are there between Vijay and Mary?**

(1) 5 (2) 6 (3) 7 (4) 8 (5) None of these

**Explanation:**

Number of persons between Vijay and Jack = 48 – (14 + 17) = 17.

Now, Mary lies in middle of these 17 persons i.e., at the ninth position.

So, number of persons between Vijay and Mary = 8.