Loading…
Free Content10 MCQs
Imagine you are standing in a line for a roller coaster. You want to know where you are standing. Are you 5th from the front or 10th from the back? Ranking and Order helps us understand these positions in a group or a line. It's like finding your spot in a big queue! This topic is super important for exams because it teaches you to think clearly about arrangements and numbers.
When you are given a person's rank from both sides (like left and right, or top and bottom) and need to find the total number of people, simply add both ranks and then subtract 1.
This trick works because the person's position is counted twice when you add ranks from both ends. Subtracting 1 makes sure they are counted only once for the total.
If you know the total people in a line and a person's rank from one side, and you need their rank from the other side, use this simple method.
Just take the total, subtract the known rank, and then add 1. This is faster than drawing a line every time!
When two people interchange their positions, and you are given the new rank of one person and the old rank of the other, you can quickly find the total.
Just add the new rank of the first person (from their side) to the original rank of the second person (from their side), and then subtract 1. It's like using the 'Count Once' trick on the new combined information.
To find the number of people between two persons, first add their ranks from the same side (e.g., both from left or both from right, if converted). If this sum is less than the total, it's a 'no overlap' case: subtract the sum from the total. If the sum is more than the total, it's an 'overlap' case: subtract total from sum, then subtract 2 (for the two people themselves).
This helps you quickly figure out which formula to use without confusion.
Ranking and Order is all about finding positions. Think of it like this: if you have a line of friends, where does each friend stand? We use numbers to tell us their place. This topic helps us solve problems where we need to find out the **total number of people** in a line, or the **position of one person** from the other end, or even how many people are **sitting between two people**.
We mostly deal with things arranged in a **straight line** (linear arrangement). Sometimes, questions might involve a circle, but the main idea stays the same: figuring out 'who is where'.
This is the most common type of question. If you know a person's rank from both ends of a line, you can find the total. Let's say your friend, **Riya**, is 5th from the left and 7th from the right in a line. If you add 5 and 7, you get 12. But Riya has been counted twice! Once as the 5th from the left, and once as the 7th from the right. So, to find the actual total, we need to subtract 1 from the sum. So, **12 - 1 = 11** people in the line.
What if you know the total number of people and a person's rank from only one side? You can easily find their rank from the other side. Let's say there are **20 students** in a class. Your friend, **Anuj**, is 8th from the top. To find his rank from the bottom, you first subtract his rank from the total: **20 - 8 = 12**. Now, this '12' tells you how many people are *after* Anuj. To find Anuj's rank from the bottom, you add 1 to this number. So, **12 + 1 = 13**. Anuj is 13th from the bottom.
This can be a bit tricky! There are two main situations:
Sometimes, two people swap their places in the line. This type of problem is interesting. If **A** is 10th from the left and **B** is 15th from the right. They swap places. Now, **A** becomes 18th from the left. We need to find the total number of people. When **A** moves to B's old spot, A's new position from the left is 18th. We know B's original position from the right was 15th. So, at the spot where A is now (18th from left), we also know its original position from the right (which was B's original position, 15th). So, we can use the main total formula: **Total = (New Rank of A from Left) + (Original Rank of B from Right) - 1 = 18 + 15 - 1 = 32 people**.
Understanding these basic ideas will help you solve almost any Ranking and Order problem easily! Just remember to always think about who is being counted and how many times.
Total Persons in a Line (Single Person)
T = (Rank from Left) + (Rank from Right) - 1Rank from Opposite End
Rank from Other Side = Total Persons - Rank from One Side + 1Persons Between Two (No Overlap)
Persons Between = Total Persons - (Rank of A + Rank of B)Persons Between Two (Overlap Case)
Persons Between = (Rank of A + Rank of B) - Total Persons - 2Total Persons After Position Swap
Total = (New Rank of 1st Person from Left) + (Original Rank of 2nd Person from Right) - 1| Scenario | What to Find | Key Idea | Formula Used |
|---|---|---|---|
| Single person, both ranks known | Total persons | Person counted twice, subtract 1 | Total = (L + R) - 1 |
| Total known, one rank known | Rank from other side | Subtract rank, then add 1 | Other Rank = Total - One Rank + 1 |
| Two people, ranks don't overlap | Persons between them | Total minus sum of ranks | Between = Total - (R1 + R2) |
| Two people, ranks overlap | Persons between them | Sum of ranks minus total minus 2 | Between = (R1 + R2) - Total - 2 |
| Two people swap positions | Total persons | One new rank, one old rank, apply total formula | Total = (New R1 + Old R2) - 1 |
Q: In a line of people, Rohan is 12th from the left end and 18th from the right end. How many people are there in the line?
Q: In a row of 45 students, Shreya is 20th from the top. What is her rank from the bottom?
Q: In a queue, Amit is 15th from the front and Bimal is 25th from the back. There are 50 people in the queue. How many people are between Amit and Bimal?
Q: In a line of boys, Ram is 16th from the left and Shyam is 18th from the right. If they interchange their positions, Ram becomes 25th from the left. What is the total number of boys in the line?
In a gaming tournament, your friend Rahul ranked 8th from the top and 15th from the bottom. How many players were in that tournament?
A cricket player, Rohit, is ranked 30th among all batsmen. If there are 50 batsmen in total, what is Rohit's rank from the last?
At a bus stop, Priya is 7th from the front and Kartik is 12th from the back. If there are 25 people in total in the queue, how many people are standing between Priya and Kartik?
In a class, Aryan is 9th from the top and Shruti is 13th from the bottom. If they swap their positions, Aryan becomes 17th from the top. What is the total strength of the class?
In a row, A is 10th from the left and B is 15th from the right. If there are exactly 6 people between A and B, what is the minimum number of people in the row?
1In a row of boys, Deepak is 9th from the left and Prakash is 18th from the right. If there are 36 boys in the row, what is Deepak's rank from the right?
2In a row of 30 students, Reena is 15th from the front. What is her rank from the back?
3Anjali is 12th from the left and 20th from the right in a line. How many people are there in the line?
4In a class of 50 students, Divya's rank is 10th from the top. If 5 students fail, what is Divya's rank from the bottom among the passed students?
5In a row of girls, Meena is 8th from the left and Seema is 17th from the right. If there are 30 girls in the row, how many girls are between Meena and Seema?
6In a row of students, P is 15th from the left and Q is 10th from the right. If there are 20 students in the row, how many students are between P and Q?
7In a row, A is 10th from the left and B is 15th from the right. If they interchange their positions, A becomes 18th from the left. What is B's new position from the right?
8In a line of 40 students, M is 13th from the top. N is 4th from the bottom. How many students are between M and N?
9In a row of trees, one tree is 7th from the left end and 14th from the right end. How many trees are there in the row?
10If Rohan is 18th in a class of 40 students from the top, and there are 5 students below him who have failed. What is Rohan's rank from the bottom among the passed students?
When you are given a person's rank from both sides (like left and right, or top and bottom) and need to find the total number of people, simply add both ranks and then subtract 1.
This trick works because the person's position is counted twice when you add ranks from both ends. Subtracting 1 makes sure they are counted only once for the total.
If you know the total people in a line and a person's rank from one side, and you need their rank from the other side, use this simple method.
Just take the total, subtract the known rank, and then add 1. This is faster than drawing a line every time!
When two people interchange their positions, and you are given the new rank of one person and the old rank of the other, you can quickly find the total.
Just add the new rank of the first person (from their side) to the original rank of the second person (from their side), and then subtract 1. It's like using the 'Count Once' trick on the new combined information.
To find the number of people between two persons, first add their ranks from the same side (e.g., both from left or both from right, if converted). If this sum is less than the total, it's a 'no overlap' case: subtract the sum from the total. If the sum is more than the total, it's an 'overlap' case: subtract total from sum, then subtract 2 (for the two people themselves).
This helps you quickly figure out which formula to use without confusion.
T = (Rank from Left) + (Rank from Right) - 1Rank from Other Side = Total Persons - Rank from One Side + 1Persons Between = Total Persons - (Rank of A + Rank of B)+2 more formulas below