Rule #4
Non-predictable order/ranking.
If the data in the question provides only then information of position different objects or persons then it is impossible to find the total number of objects or people in a group or class. As the cases can either be an overlapping or non-overlapping one. In such a situation the final answer will always be found. Save the time by not trying to solve these type of questions.
Example 5:
Deepavali or Diwali a festival lights in India. One can find the row of lamps in every house these days. Chaitra lights a row of the lamp in her home. A square-shaped lamp is at 18th from left and a circular shaped lamp is at 25th position in a row from right. Find the total number of lamp Chaitra had lit?
A.27
B.30
C.43
D. Cannot be determined.
Solution:
The scenario can be either be of Overlapping or non-overlapping one. Hence the correct answer is option D.
Rule#5
Swapping of position to find the order/ ranking
In this section, the placement or the position of the two objects/persons are interchanged. The position of the two people or objects is examined before and after the interchanged.
The place value or the position of the second person from the same side as before interchanging
= Position of 2nd person from the same side before interchanging + (Position of 1st person after interchanging – position of 1st person before interchanging from the same side)
Example 6:
Soldiers Punita and Mitali and are standing in a row of female soldiers. Punita is 18th from the left side of the row and Mitali is 24th from the right side of the row. If they interchange their positions Punita becomes 31st from left. Find:
- The new position of Mitali from the right side
- The total number of female soldiers in a row.
- Number of soilders stadning between between Punita & Mitali
Solution:1
The new position of Mithali from right side = Position of Mithali from the right side before interchanging + (Position of Punita from the left side after interchanging – Position of Punita from the left side before interchanging)
New position of Mithali from right side = 24 + (31 – 18) = 24 + 13 = 37
The new position of Mithali is 37th.
Solution 2:
The total number of person between A and B can be found in two different ways.
- Total no. of persons = (A’s position from right before interchanging + A’s position from left before interchanging) – 1
or
- Total no. of persons = (B’s position from right after interchanging + A’s position from left before interchanging) – 1
Since we don’t know the position of Punita from right before interchanging. We can’t use the first method. We can use the second method as we know both the values.
The Total number of female soldiers = (Mithali’s position from right before interchanging + Punita’s position from left before interchanging) – 1
= 37+18 -1 = 54.
Solution 3:
To find the total number of people between any two persons.
No. of persons between A & B = (Position of A from left after interchanging– Position of A from left before interchanging) – 1
The total numbers of soldiers between Punita & Mithali = (Position of Punita from left after interchanging– Position of Punita from left before interchanging) – 1
= (31 – 18) – 1 = 13 – 1 = 12
Rule#6
If positions of two objects from opposite sides of the row are known there is a third object right in the middle of the two, then the total number of objects can be evaluated based on the position of the third object.
Case 1:
The position of the third object is known from both the sides
Case 2:
The position of the third object is known from either of the sides.
Example 7:
There is a pride of lions and its cubs in a row, the position of eldest lioness from the left side of the row is 9th & position of youngest lioness from the right side of the row is 8th. If the newborn cub is sitting just in the middle of eldest & youngest and position of cub from the left side of the row is 15th. Find the total number of lions the row?
Solution:
Position of a cub from left is 15th and the eldest lioness from left is 9th so there are 15 – 9 – 1 = 5 lions are sitting between eldest and youngest lioness. As the cub is sitting in the middle of the eldest and youngest lioness so there must also be 5 persons sitting between the youngest lioness and a cub.
Thus position of a cub from right =
Position of youngest from right + 5 + 1 =
= 8 + 6 = 14
Total number of lions = (Sum of positions of cubs from both sides – 1)
= (15 + 14) – 1 = 29 – 1 = 28
Rule#7
To find the minimum number of members in the group.
The Minimum number of persons = Sum of positions of persons from both sides – Persons between them – 2.
Example 8:
If the position of A from the left side of a row is 15th and position of B from the right side of a row is 19th and only 1 person is sitting in the middle of A & B. Find the minimum number of persons that can be seated in this row?
Solution:
The total number of persons = 15 + 19 – 1 – 2 = 31.
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