Order and Ranking: Types, Methods and Examples
Order and ranking is a reasoning topic in which the position of a person or an object in a row is described from one or both ends, and the candidate has to find the total number, the position from the other end, or the arrangement in order of height, age, marks or weight. The question may be given as a plain statement such as "in a row of students, A is seventh from the left and fifth from the right", or as a comparison puzzle such as "B is taller than C but shorter than A". The candidate must apply a few simple formulas and arrange the given information carefully to reach the answer.
The special feature of order and ranking is that it is quick and formula based when the row is linear, but becomes a test of careful reading when several people are compared. This article gives a complete deep-study revision of the topic. It explains the basic terms, the standard formulas, the types of questions, the comparison method, the useful shortcuts, the step-by-step approach, the common mistakes and a practical preparation plan so that the topic becomes an easy and reliable source of marks in APSC, ADRE, Assam Police, SSC and Railway examinations.
Basic Terms
- Position from left: the rank counted from the left end of a row.
- Position from right: the rank counted from the right end of a row.
- Total number: the number of persons or objects in the row.
- Interchange: a case in which two persons exchange their positions and new ranks are given.
- Overlap: a case in which the two given ranks add up to more than the total number of persons.
- Comparison puzzle: a question in which people are compared by height, age, marks or weight.
- Ascending order: arrangement from smallest to largest, such as shortest to tallest.
- Descending order: arrangement from largest to smallest, such as tallest to shortest.
- Adjacent: two persons standing next to each other in a row.
- Extreme end: the first or the last position in a row.
Core Concepts and Formulas
- Total = (rank from left) + (rank from right) - 1, when the two ranks refer to the same person.
- Rank from right = Total - (rank from left) + 1.
- Rank from left = Total - (rank from right) + 1.
- Number of persons between two persons = difference of their ranks - 1, when both ranks are from the same end.
- If two persons are at fixed ranks from the same end and the total is asked, use the formula carefully with the number between them.
- Total = (number before a person) + (number after the same person) + 1.
- In comparison puzzles, arrange the persons in a line according to the given statements, taking one relation at a time.
- When two ranks of the same person add up to more than the total, the sides overlap and the total must be calculated keeping the overlap in mind.
Linear Row Questions
The most common question gives the rank of a person from both ends of a row and asks for the total number of persons. If a boy is ninth from the left and seventh from the right, the total is 9 + 7 - 1 = 15. The "-1" is used because the boy himself is counted in both ranks and must not be counted twice. If instead the total is given along with one rank, the other rank is found by subtracting and adding one. This single formula solves the majority of row questions, so a candidate should memorise it and understand why it works rather than applying it blindly.
Interchange of Positions
In an interchange question, two persons in a row exchange their places and the new rank of one person is given, and the candidate must find the total or the other rank. The key is to notice that after the interchange, the position that one person gives up is the position that the other person now occupies. By comparing the old rank of one person with the new rank of the other, the total can be found. Such questions look confusing but become simple once the candidate draws a small row and marks the two persons and their exchange.
Comparison and Arrangement Questions
In a comparison puzzle, several statements compare persons by height, age, marks or weight, and the candidate must arrange them in order or find who is tallest, youngest or highest. The safe method is to write the names and connect them with greater-than and less-than signs, then order them step by step. For example, "A is taller than B, B is taller than C, and D is taller than A" gives the order D, A, B, C from tallest to shortest. The candidate should place each new relation into the line already made and must read words such as "taller than", "shorter than", "older than" and "younger than" very carefully, because a single reversed word changes the whole answer.
Steps to Solve an Order and Ranking Question
First, read the question and identify whether it is a row question, an interchange question or a comparison puzzle. Second, draw a rough line or write the names and note the given ranks or comparisons. Third, apply the correct formula for the row type, or place the relations one by one for the comparison type. Fourth, check whether the given ranks overlap or whether a person appears in two statements. Finally, verify the answer against the options by counting the positions once again, and make sure the direction from which the rank is counted is clearly understood.
Examination Trends
In competitive examinations, order and ranking questions most often ask for the total number of persons in a row, the rank from the opposite end, the number of persons between two persons, and the arrangement by height, age or marks. Some papers combine ranking with puzzle sets about seating, and a few use the interchange form. Because the calculations are simple, the marks depend on careful reading and on using the correct formula. Previous years' papers show that speed with the total formula and accuracy with comparison statements are the two skills that matter most.
Common Mistakes to Avoid
- Do not forget the "-1" when adding the ranks of the same person from both ends.
- Do not mix up left and right or top and bottom while reading a rank.
- Do not ignore the word "between", which requires subtracting one from the difference of ranks.
- In comparison puzzles, do not reverse "taller than" or "younger than" while arranging.
- Do not count a person twice when the two ranks overlap in a short row.
How to Prepare This Topic
Begin by memorising the three basic formulas and practising at least twenty simple row questions until they become automatic. Then solve interchange questions and questions that ask for the number of persons between two given persons. After that, practise comparison puzzles with four or five persons, arranging them by height, age, marks and weight. For every mistake, redraw the row or the comparison line and find out where the direction went wrong. Finally, attempt previous years' papers under timed conditions so that both speed and accuracy improve.
Frequently Asked Questions
What is the formula for total number in a row?
When the rank of the same person is given from both ends, the total number is (rank from left) + (rank from right) minus one. The one is subtracted because the person is counted in both ranks.
How do I find the rank from the other end?
If the total number and one rank are known, the rank from the other end is total minus the given rank plus one.
How many persons are between two ranks?
When both ranks are counted from the same end, the number of persons between them is the difference of the two ranks minus one.
How do I solve comparison puzzles quickly?
Write the names and connect them with greater-than and less-than signs from the statements, then place each new relation into the line already made until the whole order is clear.
What should I be careful about in interchange questions?
Remember that after the exchange, the position one person leaves is the position the other person now occupies, so compare the old rank of one with the new rank of the other to find the total.