Note:

1) Read the statement line by line and apply the cases as explained below.

2) Position can be from either sides of row and rank is always from top or bottom of the row

Here, different types of ordering & ranking arrangement questions are explained below with the

help of different examples. By grasping each type, you can have a complete command over this

topic and ensure 3-5 marks in your kitty.

Type 1

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

side) – 1}

OR

2) Position of a person from opposite side = {(Total no. of persons – Position of same person from

given side) +1}

  E.g.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?

Solution:

Total no. of students = (Position of A from left + Position of A from right) -1⇒Total no. of students = (27 + 34) – 1 = 61 – 1 = 60

  E.g. 2)  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?

Solution:

Position of A from right side = {(Total no. of persons – Position of A from left side) + 1}⇒Position of A from right side = (16 – 12) + 1 = 4 + 1 = 5th

 

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

2) No. of persons after or before the given person in a row = Total no. of persons – Position of

same person from other side

E.g.1) In a row of persons, position of A from left side of the row is 27th and there are 5 persons

after A in the row. Find total no. of persons in the row?

Solution:

No. of persons in the row = Position of A from left + No. of persons after A⇒ Total no. of persons = 27 + 5 = 32

E.g.2) In a row of 18 persons, position of A from left side of the row is 6th. Find the no. of persons

after A in the row?

Solution:

No. of persons after A = Total no. of persons – Position of A from left⇒ No. of persons after A in the row = 18 – 6 = 12

 

 Type 3

When the positions 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 positions of the two persons from opposite ends <

total number of persons

2. When there is overlapping: i.e. the sum of positions 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 positions of two

different persons from opposite sides)

E.g.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?

Solution: Here Sum of positions of A & B from opposite ends = 15 + 20 = 35 < Total no. of

persons∴ No. of persons between A & B = Total no. of students – (Position of A from left + Position of B

from right)⇒ No. of persons between A & B = 54 – (15+20) = 54 – 35 = 19

Case ii)

No. of students between two different persons = (Sum of positions of two different persons from

opposite sides) – Total no. of students  – 2

E.g.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?

Solution: Here Sum of positions of A & B from opposite ends = 35 + 22 = 57 > Total no. of

persons∴ No. of persons between A & B = (Position of A from left + Position of B from right) – Total no. of

students – 2⇒ No. of persons between A & B = (35+22) – 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.

E.g. 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?

Solution: Cannot be determined as position of different persons is given from the same side.

 

Type 5

Positions of two persons is 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 2ndperson 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 Þ 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 Þ Difference in the position of common person whose

position from same side before and after interchanging is given then subtract 1

E.g. 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

1. i) New position of B from right side

ii) Total no. of persons

iii) No. of persons between A & B

Solution:

1. 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)⇒ New position of B from right side = 24 + (31 – 18) = 24 + 13 = 37th

         ii) Total no. of persons = (A’s position from right before interchanging + A’s position from

left           before interchanging) – 1⇒ Total no. of persons = (B’s position from right after interchanging + A’s position from left

before interchanging) – 1⇒ Total no. of persons = (24 + 31) – 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⇒ No. of persons between A & B = (31 – 18) – 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

1. i) When position of third person sitting is given from either side of row

2. 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

E.g. 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 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?

 Solution: Position of C from left is 15th and A from left is 9th so there are (15 – 9 – 1 = 5) 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)⇒ Total no. of students = (15 + 14) – 1 = 29 – 1 = 28

E.g. 2) 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 middle of A & B and position of C from A is 7th. Find total no.

of persons in the row?

Solution: Position of C from Left = Position of A from left + Position of C from A = 11 + 7 = 18 th

Given C is 7th from A and C is sitting in middle of A and B then 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)⇒ Total no. of students = (18 + 26) – 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

E.g. 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 & B. Find the minimum number of persons that can

be seated in this row?

Solution: Total no. of persons = 15 + 19 – 1 – 2 = 31

 

Type 8

These are ordering type questions. In this type of question, it is given that there are several

people living in an n-storey building. Some information will be given about the relative positions

of one above or below the other. You need to find which floor each person lives on. These are

almost similar to seating arrangement questions.  However, you may be required to apply the

rules you learnt above, in these problems.Input output

HOW TO SOLVE

These questions can be solved by the following methods:

1. We can solve these questions by writing each step of the given input on paper.

Remember – do not write the complete word each time; to save time, just write the first letter or however

many letters of each word you need to uniquely identify it.

Example:

Input:   32   pure   girl   beautiful   49    63    78    random   rickshaw

Label:   32      P        G          B           49    63    78        Ra         Ri

2. We could go for a shorter method where instead of writing each step again and again we number each

word/number of the input as per their position in each step. So if the arrangement follows a “number-

descending-from-left-and-letters-ascending-from-right-alternately-pattern”, we need to number these as

follows:

Clearly the pattern is, ‘send the biggest number left’. In the next step, send the highest word right.

Continue the pattern till the input is completely rearranged.

To minimize the steps, let us look at all the elements on the basis of their positions. We only need to see

the first two steps and the output to figure out which number/word goes where. The order in which the

element gets rearranged is the number each element gets.

INPUT:   32        pure     girl       beautiful          49        63        78        rickshaw          random

LABEL:     7           6           8           9                       5           3          1             2                       4

Since ‘78’ is the first element that will be rearranged according to the pattern, it will be labeled 1. The next

element to be rearranged will be ‘rickshaw’. So it will be labeled 2. The next element to be rearranged will

be the next highest number. So without even writing out the remaining steps you could label ‘63’ as 3. And

similarly ‘random’ would become 4. And so on and so forth.

While rearranging by this method, keep the following four cases in mind:

Case 1: When we go in single direction, i.e. words/digits are arranged either from left to right or right to

left. In this case, auto filling of words/digits could take place because some numbers/words arrange

themselves. So how do we go about numbering our elements in this case? For convenience’s sake, let

us think of all the elements being arranged left to right.

1. Number each word/number in the manner shown above as per their order of arrangement in accordance with the pattern depicted in the question. Think of it as a step-by-step process. After each numbering, you need to stop and check.

2. After you identify the first element, number it (1). Then identify the second element. Check all the elements to its left. Have you numbered all of them yet? If yes, then number this one (1a). If not, then number it (2). Then identify the third element. Check all the elements to its left. Have you numbered all of them yet? If yes, then this does not get a new step number. If no, then it gets a fresh step number. And the process continues. Here is an illustration.

Step VII is the last step of the input

Q. Following the above pattern, how many steps will be required to complete the arrangement for the

below given input?

84  out   sown   even   35   54   around  46

Solution:

Input: In the given illustration, the words/digits are being arranged in the following manner: the lowest

digit is arranged at leftmost of the sentence and all others are shifted to the right side as it is and in

second step, highest word of dictionary is arranged right of the previously arranged number and so on. The

next higher digit and next highest word is arranged in subsequent pair of steps.

Here is how you would go about numbering these elements. Note that underlined elements represent those

ones to the left that you haven’t numbered yet.

Here, 6a and 6b are not given further values as at the time of filling, as all elements to the left of these two

have been filled already. Hence, these two entities are arranged automatically in step 6. In addition, step 6

is the last step of the input, so six steps are required to complete the arrangement.

NOTE: Now whichever step is asked in the question, take the part of the solution up to the required step

number to get the answer. Arrange the numbered elements according to their labels, and shift the

remaining to the right, while leaving their order unchanged.

NOTE:   If the rearrangement is to be done from the right, the process of checking would be reversed. Now

instead of checking to the left, you would have to check to the right to see if there are any unnumbered

elements.

Case 2:   When we go in both directions, with elements filling in from the inside, auto filling could still

take place. So we need to take that into account when numbering. Based on which direction the element

goes, it is numbered with an L (left) or an R (right) attached to it. When considering items labeled with L,

check to see if there are any unlabeled elements to its left and when considering items labeled with R,

check to see if there are any unlabeled elements to its right.

Step III is the final step of the rearrangement.

Q. Following the above pattern, how many steps will be required to complete the arrangement for the

below given input?

goat  out   34   59   set   75   peon   28

Solution:

Input: The rearrangement clearly happens from both directions simultaneously, but from the inside. The

fact that the rearrangement is happening from the inside makes a huge difference. The numbers are

arranged in ascending order from the left and the words are arranged in descending order of their

appearance in the dictionary, but from the right.

Here is how you go about numbering these elements. Note that underlined elements represent those ones

to the left of the ‘L’ elements that you haven’t numbered yet. And the italicized elements represent the

ones to the right of the ‘R’ elements that you haven’t numbered yet.

Now, it is easy to answer the question based on the numbering. The answer is three steps.

Q. Following the above pattern, what will be the second step after rearrangement for the below given

input?

goat  out   34   59   set   75   peon   28

Solution:

The underlined elements represent the remaining elements unchanged in order.

 Case 3: When we go in both directions with elements filling in from the outside, i.e. we place

digits/numbers left to the left most word/ right to the right most word. In this case, noauto filling of

digits/numbers takes place i.e. each word is numbered separately. Keep in mind the following:

1. Number of pairs of words/digits is equal to the number of steps.

2. Identify the pattern in the input rearrangement. Then number the elements going left in their pattern order with 1L, 2L, 3L and so on. And number the elements going right in their pattern order with 1R, 2R,3R and so on.

3. There is no auto filling, so there is no need to check step by step. The numbering can be done in one go.

STEP V is the last step of the input.

 Q. Which is the 5th letter from right side in step V of the following input?

Input:   87       when   show    14        35        new     beat     ink       51        28

Label:   5L        5R        4R        1L        3L        3R        1R        2R      4L       2L

Solution: In the given illustration, the words/digits being arranged in the following manner: in the first

step, lowest digit and lowest word in dictionary are placed at left most and right most side respectively, of

the string and all other entities are placed as it is. Then in the 2nd step, next lowest digit and word are

arranged to the left and right of the previously arranged digit and word simultaneously and so on.

Therefore, arrangement is from left to left + right to right.

Here L1, L2 so on are used to represent left side and R1, R2 so on to represent right side.

Hence step 5 of the input is

Step 5:   87     51    35    28    14    beat    ink    new    show    when

So 5th from the right side is ‘beat’

NOTE: In this case 5th from right is not R5, but R1. So be careful while answering this type of question.

Count backwards from the highest number label of that step in such cases.

Case 4: In mixed form i.e. both case 1 and 2 are used in one input then both the rules are used for each

side

NOTE: If pairing of words and digits/words and words/ digits and digits is observed i.e. both are placed

simultaneously in each step and in case if one is auto filled & other is not then no step is skipped.

Its a blessing to have these Time saving short Tricks for Input Output in Reasoning just when the exam is

just few days away. Share this knowledge with your fellow mates and let them also benefit from the same.