cHAPTER-5
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 -
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:
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:
Maximum person
Minimum person
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.
Ans: (4)
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