Order & Ranking- Reasoning
It is very interesting topic in which position of an object will be given from the either end(top/left/bottom/right) and you will be very expected to find out position of the same objects from another end (bottom, right ,top ,left) ,when total number of objects in a queue is given. So, here all the cases will be discussed in this article.
Type-1: When the total no. of elements is given in a queue and
the position of an element is given from the left end, How you find the position from the right end of the
same element.
We can best understand
this pattern with a couple of examples.
Ex1. In a row of 16
students, If Mira’s position is 7th from the left end then what is her position
from the right end?
Sol- There are 16 students in
a row i.e., Total = 16
Mira position from left end = 7
Mira
position from right end = (Total +1) – position from left end
= (16 +1) – 7 = 17 -7
=10 i.e., 10th from right end.
Trick–
Position from Right end = (Total no. of elements+1) – Position from left end.
Ex2. In a class of 125
Students, The position of Suresh is 45th from the top. Find his
position in the class from the bottom.
Sol- Don’t be confused with the word
top just consider it as Left end and Bottom as Right end while attempting
question.
Left end position of
Suresh = 45
Total = 125
Right end position of
Suresh= (125+1) – 45 = 126 – 45 = 81.
Trick- Treat Top as Left and Bottom as Right for doing
questions of Vertical line
arrangement/ranking.
TYPE-2: When
Total number of elements are given and position of an element from right end is
given then how you find position from left end?
We can best understand with a couple of examples.
EX1. In a
row of 26 students, the position of Kamal is 15th from right
end then what is his position from left
end in a queue?
Sol- Here
total is given = 26
Right end position = 15
Left end position= (Total + 1) – Right
end position
= (26 +1) – 15 =
27 -12 = 15.
Trick-Position
from left end of element in a queue= (Total no. of elements+1) – Right end
position of the same element.
Ex2. In a class
of 245 students, the Position of Mohan from the bottom is 100 then what is his position from the top.
Sol – Here
again, we got the word “Top”
Just replace it with the
left end and Bottom
as “Right”.
Total= 245
Right end=
100
Left end
/Top end position of Mohan = (Total +1) – right end position/Bottom end
position
=(245+1) – 100 = 246 – 100 = 146
Trick-Position
from left end of element in a queue= (Total no. of elements+1) – Right end
position of the same element.
Ex2. In a class of 245 students, the Position of Mohan from the bottom is 100 then what is his position from the top.
Sol – Here
again, we got the word “Top”
Just replace it with the
left end and Bottom
as “Right”.
Total= 245
Right end=
100
Left end
/Top end position of Mohan = (Total +1) – right end position/Bottom end
position
=(245+1) – 100 = 246 – 100 = 146
TYPE-3: When the Left end position and the
Right end position have been given, then how you will find the total number of
elements in a queue?
To deal with such type of
above mentioned all situations (Type1, type2,&type3) just keep one relation
in your mind.
Trick - Position from the left end/ Position
from Top of the element + Position from the
right end/ position from the Bottom of
the same element – 1 = Total No. of Elements.
We can better understand with a couple of examples.
Ex1.Akash ranks seventh from the top and
twenty-sixth from the bottom in a class. How many students are there in the
class?
Sol- Here
Top/Left end position = 7
Bottom/ Right end position =
26
Total students = 7 + 26 – 1 = 32
Note – Use
above relation directly in any above mentioned type of questions.
Second
method-
By drawing
figure,
Clearly, the
whole class consists of:
So, total students = (6 + 1 + 25) = 32
students
Tip – First method is very handy without drawing figure, by just keeping one
relation in our mind.
Ex2.Kumud ranks 8th from the top and
34th from the bottom in a class. How many students are there in the
class?
Sol- Total =
Top/ left + Bottom/right - 1
= 8 + 34 – 1 = 41
So there are
41 students are in the class.
Note – There
is one another method of finding total number of elements present in a queue
when position of same element from both ends is given. We can best understand
with example.
Ex3.Kumud ranks 8th from the top and
34th from the bottom in a class. How many students are there in the
class?
Sol – Let us
take there are total no. of students=N.
Now try to find position of KUMUD from same end i.e., either from top end or bottom end so, Here another bottom end position we are converted into top end position, You can do reverse of it also, It will make no change in result.
Kumud's position from top end = (total + 1) – (bottom end)
= ( N+1) – 34 = N - 33
Now we got
the value from left end one is (N-33) and another is 8, which is given so both
must be equal
So, (N- 33) = 8
Or, N= 33 +
8 = 41
So, there
are 41 students are present in the classroom.
Trick of this approach-
1. Take total no. of students N.
2. Bring both positions from same end i.e., either
from top/left or bottom/right with the help of N.
2. Just equate to given position in the question.
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Type-4: To find how many elements are present
there in between two elements in a queue when their positions from left end/top
and right end/bottom are given.
Let us take a example to a better understanding of this type of question.
EX1. If the position of Suresh from the left end is 15 in a classroom
consisting 26 students while Mohan position from the right end is 6. Find how
many students are present in between both?
Sol- Just Convert the right end position into the left end
position to make the question easy.
Left end position of Mohan = (Total + 1) – right end position
= 26
+1 – 6 = 27 – 6 = 21
Now we got to know position of both persons from left end.
So, Number of students in between both = (21 – 15) – 1
= 6 – 1 = 5
Trick = Number of
elements in between = (N1 – N2) – 1
Where N1 = Position of
one element from the left end/top.
N2 = Position of another element
from the left end/top.
Where N1 > N2.
OR
Number of elements
present in between two elements = (N2 – N1) -1
Where N1 = Position of one element from the
right end/bottom.
N2 = Position of another
element from the right end/bottom.
Where N2 > N1
Note – Remember to
take both positions from either the left end/top or right end/ bottom and then subtract from bigger position
value to smaller position value at first
then finally subtract one from the result of the difference of bigger position value and
smaller position value.
Type-5: Interchange the position in a queue.
In this pattern, two persons interchange their position when they are seated in the same row/queue. To better understanding, we are taking an example to understand it better.
Ex1. In a row of girls, Kamya is fifth from the
left and Preeti is sixth from the right. When they exchange their positions,
then Kamya becomes thirteenth from the left. What will be total number of girls
in a row?
Second method-
By drawing
exact positional figure of both girls i.e.,
Here, Kamya is at the fifth position means there are 4 girls
before kamya in a row in the similar way preeti is 6th from the
right means there are 5 girls before preeti. After interchange kamya came at
the place of preeti, it is given kamya is at 13th place from left
end means there are 12 girls before kamya and after kamya there are 5 girls
also so, the total will be sum of 12 ,5 and herself kamya i.e., 1.
Thus, the row consists total of (12 + 1 + 5) = 18 girls.
Tip- Focus on position value of given element after interchange i.e., Here it is kamya whose position is given.
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