# PE 2 - Ranking | Arrangements, Ranking & Ordering

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

Samarth is ranked sixth from the top and twentieth from the bottom in a class. How many students are there in this class?

- A.
23

- B.
24

- C.
25

- D.
26

- E.
27

Answer: Option C

**Explanation** :

When certain number of people are arranged according to a particular criteira, then

Total number of people = position of a person from the top + position of the same person from bottom – 1.

∴ Number of students = 6 + 20 – 1 = 25.

Hence, option (c).

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**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of 38 boys, Ranu became 19^{th} from left when he shifted five places to the right. What was his earlier position from the right end of the row?

- A.
23

- B.
25

- C.
24

- D.
27

- E.
29

Answer: Option B

**Explanation** :

Original position of Ranu from the left = 19 – 5 = 14^{th}

The row had 38 boys.

∴ There were originally 38 − 14 = 24 people to his right.

Hence, his earlier position from the right end = 24 + 1 = 25^{th}.

Hence, option (b).

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**PE 2 - Ranking | Arrangements, Ranking & Ordering**

Neha is 7 ranks ahead of Ashutosh who ranks 25^{th} in a class of 40. What is Neha’s rank from the end?

- A.
23

- B.
22

- C.
24

- D.
25

- E.
Cannot be determined

Answer: Option A

**Explanation** :

Ashutosh ranks 25^{th} and Neha is 7 ranks ahead of Ashutosh.

∴ Neha ranks 25 − 7 = 18^{th}

Number of students behind Neha in rank = 40 – 18 = 22

Hence, Neha’s rank from the last = 22 + 1 = 23^{rd}

Hence, option (a).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of boys, Alok is 4^{th} from left and Yash is 30^{th} from right. If they exchange their positions, Alok becomes 21^{st} from left. How many boys are there in the row?

- A.
45

- B.
47

- C.
50

- D.
57

- E.
59

Answer: Option C

**Explanation** :

After the exchange, Alok comes to Yash’s position and becomes 21^{st} from left.

The same position also corresponds to the 30^{th} position from right.

∴ Total number of boys in the row = (position of Yash from left) + (position of Yash from right) – 1

= 21 + 30 – 1 = 50.

Hence, option (c).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

Bhanu is ranked 15^{th} from the top and 25^{th} from the bottom in a class. If three new students join the class, how many students are now in this class?

- A.
43

- B.
41

- C.
42

- D.
38

- E.
None of these

Answer: Option C

**Explanation** :

Original number of students = position from top + position from bottom − 1

= 15 + 25 − 1 = 39

When three new students join, new total = 39 + 3 = 42.

Hence, option (c).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of boys and girls, Paras is 17^{th} from left and Rekha is 32^{nd} from right. If they interchange positions, Paras becomes 26^{th} from left. How many boys are there in the row?

- A.
51

- B.
50

- C.
49

- D.
52

- E.
Cannot be determined

Answer: Option B

**Explanation** :

In this question we can find out the total number of people in the row.

Since no data is given related to number of boys or girls we won’t be able to find the exact number of boys or girls.

Hence, the number of boys cannot be found.

Hence, option (d).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of girls, Ranya is 15^{th} from left and Tanya is 19th from right. If Ranya is 19^{th} from right, what is the position of Tanya from left?

- A.
19

- B.
17

- C.
15

- D.
18

- E.
None of these

Answer: Option C

**Explanation** :

Total number of people = position of a person from the left + position of the same person from right – 1.

If the position of A from left and right is known, and the position of B from any one end is known, the position of B from the other end can also be found.

∴ Ranya’s position from left + Ranya’s position from right = Tanya’s position from left + Tanya’s position from right

∴ 15 + 19 = Tanya’s position from left + 19

∴ Position of Tanya from left = 15^{th}

Hence, option (c).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of boys, Anay is 14^{th} from the end and 17^{th} from the start. In another row of girls, Pooja is 16^{th} from the start and 11^{th} from the end. How many boys and girls are there in both the rows together?

- A.
58

- B.
57

- C.
55

- D.
None of these

Answer: Option D

**Explanation** :

Total boys in Anay’s row = 14 + 17 − 1 = 30

Total girls in Pooja’s row = 16 + 11 − 1 = 26

∴ Total boys and girls in both rows = 30 + 26 = 56.

Hence, option (d).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of boys facing north, A is 21^{st} from the left and B is 9th from the right. C is 5^{th} to the right of A and 7^{th} to the left of B. How many boys are there in the row?

- A.
38

- B.
39

- C.
40

- D.
41

- E.
None of these

Answer: Option D

**Explanation** :

A is 21^{st} from the left end and C is 5^{th} to the right of A. So, C is 21 + 5 = 26^{th} from the left end.

B is 9^{th} from the right end and C is 7^{th} to the left of B. So, C is 9 + 7 = 16^{th} from the right end.

∴ Total number of boys in the row = 26 + 16 − 1 = 41.

Hence, option (d).

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**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a queue, Mayank is 8^{th} from the front while Ankita is 16^{th} from behind. Astha is exactly in between the two. If there are 25 people in the queue, what is Astha’s position from the front?

- A.
7

- B.
9

- C.
11

- D.
12

Answer: Option B

**Explanation** :

Ankita is 16^{th} from behind and there are 25 people in the queue.

∴ Ankita’ position from front = 25 + 1 − 16 = 10^{th}

Mayank is 8^{th} from front and Astha is exactly between Mayank and Ankita.

∴ Astha is 9^{th} from front.

Hence, option (b).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a class of 36 children, Jaspreet’s rank is 18th from the bottom. Disha’s rank is 5th from the top. Vihaan’s rank is exactly between Jaspreet and Disha’s rank. What is Vihaan’s rank from the bottom?

- A.
25

^{th} - B.
28

^{th} - C.
26

^{th} - D.
15

^{th} - E.
None of these

Answer: Option A

**Explanation** :

There are 36 children in all and Disha is 5^{th} from the top.

∴ Disha’s rank from bottom = 36 − 5 + 1 = 32^{nd}.

Thus, Disha is 14 places away from Jaspreet.

Vihaan is exactly between Jaspreet and Disha.

Hence, Vihaan’s rank from bottom = 18 + (14/2) = 18 + 7 = 25^{th}

Hence, option (a).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a queue, Rahul is 19th from the front while Dinesh is 33rd from the end. Shubham is exactly between the two. If there are 85 people in the queue, what position does Shubham occupy from the front?

- A.
35

- B.
37

- C.
38

- D.
39

- E.
50

Answer: Option C

**Explanation** :

Rahul is 19^{th} from the fron and Dinesh is 33^{rd} from the end. There are 85 people in the queue.

Number of people between Rahul and Dinesh = 85 – 19 – 33 = 33

Shubham is the exactly between the Rahul and Dinesh, hence Shubham is (33 + 1)/2 = 17 places away from either Rahul or Dinesh.

Rahul---16 people---Shubham---16 people---Dinesh

∴ Shubham’s position from the from = 19 + 17 = 36^{th}.

Hence, option (c).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of students facing south, Pavitra is exactly between the two ends of the row. Kajal is 5th to the left of Pavitra. Animesh is 17th to the right of Kajal. What is Animesh’s position from the left end of the row?

- A.
15

- B.
22

- C.
23

- D.
Cannot be determined

- E.
None of these

Answer: Option D

**Explanation** :

Since the number of students in the row is not known, the position of Animesh cannot be found.

Hence, option (d).

Workspace:

**PE 2 - Ranking | Arrangements, Ranking & Ordering**

In a row of boys Bhanu is 21st from the left and Viru is 19th from the right. When they interchange positions, Viru becomes 30th from the right. What is the new position of Bhanu from the left?

- A.
32

- B.
35

- C.
38

- D.
31

- E.
34

Answer: Option A

**Explanation** :

Initially Bhanu was 21^{st} from the left. After interchanging position same position (occupied by Viru now) is 30^{th} from the right.

∴ Total number of students = 21 + 30 – 1 = 50.

After exchange Bhanu occpies 19^{th} position from right.

∴ New position of Bhanu from left = 50 – 19 + 1 = 32^{nd}.

**Alternately,**

Viru was originally 19^{th} from the right and then became 30^{th} from the right.

∴ Viru moved left by 11 places.

∴ Bhanu also should have moved right by 11 places.

Therefore, Bhanu’s position from the left after the interchange = 21 + 11 = 32^{nd}.

Hence, option (a).

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