Core ConceptRead this first — the foundation of the topic
Number Ranking is a logical reasoning problem where you are given a series of numbers or positions, and you must determine the rank or position of a particular number or person in a sequence—either from left to right or right to left. CORE CONCEPT
In Number Ranking problems, you need to find where a number sits in a given order. The question might ask: 'What is the rank of number X from the left?' or 'If we reverse the sequence, what becomes the position of Y?' The key is to count carefully and apply simple directional rules. KEY RULES & PROPERTIES
1. Always identify the total count of numbers/items in the sequence. 2. Rank from left means counting from position 1 on the left side.
3. Rank from right means counting from position 1 on the right side (reverse counting). 4. If an item's rank from left is R, then its rank from right = (Total Count + 1) – R.
5. The middle position exists only if total count is odd. 6. Direction matters—left and right are opposite directions.
Formula BlockMemorise — at least one formula appears in every paper
Rank from Right = (Total Number of Items + 1) − Rank from Left
Rank from Left = (Total Number of Items + 1) − Rank from Right
Total Items = Rank from Left + Rank from Right − 1
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks:
- Direct rank questions: 'Find rank of X from left/right'
- Reverse rank questions: 'If reversed, what is position?'
- Both-side rank: 'A is 5th from left and 8th from right. Find total count'
- Position-based: 'How many items between positions?'
SHORTCUT/TRICK
Always use the formula: Rank from Right = (Total + 1) − Rank from Left. This avoids counting errors. If you know any two values (total and one rank), you instantly find the other.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Count total items = 8
2
Step 2
Identify rank of 60 from left = 5 (it's the 5th number)
3
Step 3
Apply formula: Rank from Right = (8 + 1) − 5 = 9 − 5 = 4
Answer: 60 is at rank 4 from the right.
Verification: From right: 92(1st), 88(2nd), 75(3rd), 60(4th) ✓
Exam TrapsCommon mistakes students make — avoid these
Students often confuse rank with count. If 60 is 5th from left, it doesn't mean 5 items are to its left—only 4 items are to its left. Rank includes the item itself.
Key Points to Remember
Rank from Right = (Total Items + 1) − Rank from Left; memorise this formula.
Rank from left = counting from position 1 starting at leftmost item.
Rank from right = reverse counting from rightmost item as position 1.
If rank from left is R and total is T, items to the left = R − 1.
Items between two ranks = |Rank₁ − Rank₂| − 1 (subtract 1 to exclude both positions).
Direction change always uses the complement formula; direct counting saves time only for small lists.
Exam-Specific Tips
In a sequence of N items, if rank from left is L, then rank from right is always (N + 1) − L.
Number of items to the left of rank R = R − 1.
Number of items to the right of rank R = N − R.
If an item is 6th from left and 4th from right, total count = 6 + 4 − 1 = 9.
Middle position in a sequence of odd numbers (e.g., 7 items) = position 4.
Between rank 3 and rank 8 in a sequence, number of items = 8 − 3 − 1 = 4.
When a sequence is reversed, rank from left becomes rank from right in the new order.
Total items = Rank from Left + Rank from Right − 1 (this is a rearrangement of the main formula).
Practice MCQs
Number Ranking — Practice Questions
15graded MCQs · easy to hard · full solution & trap analysis
In a class of 35 students, Neha is 12th from the left end and Zara is 18th from the right end. How many students are there between Neha and Zara?
Practice 2easy
In a row of 25 students, Rajesh is 8th from the left end. What is his position from the right end?
Practice 3easy
In a queue of 60 people, Vikram is 25th from the front. If 5 people leave from behind Vikram, what will be Vikram's new position from the front?
Practice 4easy
In a class of 40 students, Rajesh's rank from the top is 12th. What is Rajesh's rank from the bottom?
Practice 5easy
Among 40 students standing in a line, Priya is 15th from the left. Deepak is 10 positions to the right of Priya. What is Deepak's position from the right end?
Practice 6easy
In a ranking of 50 students, Arun is 22nd from the top. How many students are ranked below Arun?
Practice 7medium
In a class ranking, Priya is 12th from the top and 19th from the bottom. Akshay is 5 ranks below Priya. What is Akshay's rank from the top?
Practice 8medium
Seven friends are standing in a line. Rohit is 3rd from the left. Simran is 4th from the right. How many people are standing between Rohit and Simran?
Practice 9medium
Five boxes are arranged in increasing order of weight. Box C is heavier than Box A but lighter than Box D. Box B is the lightest. Box E is heavier than Box D. What is the correct order from lightest to heaviest?
Practice 10medium
In a building with 10 floors, Apartment P is on the 4th floor from the bottom. Apartment Q is on the 3rd floor from the top. Apartment R is exactly in the middle between P and Q. On which floor is Apartment R?
Practice 11medium
In a class of 45 students, when students are ranked from highest to lowest marks, Rajesh is ranked 12th from the top. If 5 students are absent on the day of ranking, what is Rajesh's rank from the bottom in the complete class of 45 students?
Practice 12hard
In a ranking of 12 students, Raj is 5 positions below Priya. If Priya's rank from the bottom is 4, what is Raj's rank from the top?
Practice 13hard
In a ranking of 12 students, Priya is ranked 5th from the top. Rahul is ranked 3 positions below Priya. Meera is ranked exactly halfway between Rahul's position and the bottom of the ranking. What is Meera's rank from the top?
Practice 14hard
In a class of 40 students, when ranked by marks, Arun is 12th from the top. Bhavna is 8 positions below Arun. Chitra is 5 positions above Bhavna. How many students are ranked below Chitra?
Practice 15hard
In a ranking of 25 employees, Priya is 9th from the top. If 3 employees are removed from the ranking (none of whom are Priya), and all employees below the removed ones shift up accordingly, what is Priya's new rank from the top if all 3 removed employees were ranked below Priya?
60-Second Revision — Number Ranking
Formula King: Rank from Right = (Total + 1) − Rank from Left. Write it once before exam starts.
Trap: Rank ≠ Count of items on one side. Rank 5 means 4 items to the left, not 5.
Quick Check: If rank from left is L and total is T, rank from right must be T + 1 − L; verify mentally.
Direction Matters: Left = normal order, Right = reverse order. Don't flip them.
Formula Rearrange: If given rank from left and right, find total = L + R − 1. Easy bonus question.
Middle Alert: In odd sequences (5, 7, 9 items), the middle rank = (Total + 1) ÷ 2.
Between Positions: Items between rank A and rank B = |A − B| − 1. Exclude endpoints.