Ranking: Positions in a Row, Interchange and Class Ranks
Ranking: Positions in a Row, Interchange and Class Ranks
Ranking questions are counting questions. Every rule follows from one fact: a person's position from the left plus the position from the right counts that person twice. NTPC asks positions and totals in a row, two people interchanging places, the number of people between two people, and class ranks with failed or absent students.
1. Formula Box
Total = position from left + position from right − 1 (same for top and bottom)
Position from right = total − position from left + 1
Two people counted from opposite ends with no overlap: people between = total − (a + b)
With overlap (a + b > total): people between = a + b − total − 2
k places to the right of the p-th from the left = (p + k)-th from the left
| Situation | Total in the class or row |
|---|---|
| Rank r from top and s from bottom among passed students | r + s − 1 passed; add failed and absent students for the class |
| After two people interchange | Use the new position of one with the old position of the other from the other end |
| Minimum people in a queue | Let the counted ranges overlap as much as the clues allow |
✗ 17th from left and 24th from right, so 41 in the row | ✓ The person is counted twice: 17 + 24 − 1 = 40
✗ In a row of 30, X is 20th from left and Y 18th from right, so 30 − 38 people are between them | ✓ The ranges overlap: 20 + 18 − 30 − 2 = 6 people between
हिंदी नोट: पंक्ति में कुल व्यक्ति = बाएँ से स्थान + दाएँ से स्थान − 1। स्थान बदलने वाले प्रश्न में नया स्थान दूसरे व्यक्ति का पुराना स्थान होता है। उत्तीर्ण छात्रों की रैंक से कुल छात्र निकालकर अनुत्तीर्ण और अनुपस्थित जोड़िए।
Exam Pointer: Verified NTPC patterns: positions and totals in a row (August 2025 UG CBT-1, June 2025 Graduate CBT-1) and ranks from top and bottom (August 2025 UG CBT-1), and two people interchanging places (June 2022 CBT-2). People-between, class ranks with failed students and minimum-queue questions had no verified NTPC shift and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Position from both ends and total
[PYQ: NTPC UG CBT-1 22-Aug-2025 Shift-2 | NTPC Graduate CBT-1 5-Jun-2025 Shift-1 | NTPC UG CBT-1 8-Aug-2025 Shift-1]
EXAM LEVEL
Q. Ravi is 17th from the left end and 24th from the right end of a row. How many people are in the row?
17 + 24 − 1 = 40.
Answer: 40
EXAMATLAS LEVEL
Q. In a row of 85 people facing north, Meena is 29th from the left. Arjun is 12 places to the right of Meena. What is Arjun's position from the right end?
Arjun is 29 + 12 = 41st from the left, so from the right he is 85 − 41 + 1 = 45th.
Answer: 45th
Pattern 2: Interchanging places
[PYQ: NTPC CBT-2 15-Jun-2022 Shift-2]
EXAM LEVEL
Q. A is 10th from the left and B is 15th from the right of a row. They interchange places, and A becomes 22nd from the left. How many people are in the row?
A now sits in B's old place, which is 22nd from the left and 15th from the right. Total = 22 + 15 − 1 = 36.
Answer: 36
EXAMATLAS LEVEL
Q. In a row, P is 14th from the left and Q is 9th from the right. After they interchange, P is 23rd from the left. Find the total in the row and the number of people between P and Q.
Q's old place is 23rd from the left and 9th from the right, so the total is 23 + 9 − 1 = 31. P and Q sit at the 14th and 23rd places from the left, so 23 − 14 − 1 = 8 people sit between them.
Answer: 31; 8
Pattern 3: People between two people
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In a row of 40, A is 12th from the left and B is 15th from the right. How many people sit between them?
B is 40 − 15 + 1 = 26th from the left. Between the 12th and 26th: 13 people.
Answer: 13
EXAMATLAS LEVEL
Q. In a row of 30, X is 20th from the left and Y is 18th from the right. How many people sit between X and Y?
Y is 30 − 18 + 1 = 13th from the left, so Y is to the left of X: the ranges overlap. Between the 13th and 20th: 20 − 13 − 1 = 6. Formula: 20 + 18 − 30 − 2 = 6.
Answer: 6
Pattern 4: Class ranks with failed and absent students
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Among the passed students, Riya is 11th from the top and 26th from the bottom. 6 students failed and 3 were absent. How many students are in the class?
Passed = 11 + 26 − 1 = 36. Class = 36 + 6 + 3 = 45.
Answer: 45
EXAMATLAS LEVEL
Q. In a class of 50, Sita ranks 18th from the top and Mohan is 8 ranks below her. Find Mohan's rank from the bottom. If 5 students ranked above Sita leave, what are their new ranks from the top?
Mohan is 26th from the top, so 50 − 26 + 1 = 25th from the bottom. With 5 students above both of them gone, Sita becomes 13th and Mohan 21st.
Answer: 25th; Sita 13th, Mohan 21st
CBT-2 LEVEL
Pattern 5: Minimum or exact number in a queue
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In a queue, A is 7th from the front and B is 9th from the back, with 4 people between them. How many people can be in the queue?
If A is ahead of B: 7 + 4 + 9 = 20. If B is ahead of A, the counts overlap: 7 + 9 − 4 − 2 = 10. The minimum is 10.
Answer: 20 or 10 (minimum 10)
EXAMATLAS LEVEL
Q. A is 5th from the front of a queue and B is 8th from the back. C stands exactly midway between A and B, with 3 people between A and C. How many are in the queue?
C is 4 places behind A, so C is 9th; B is 4 places behind C, so B is 13th from the front. B is also 8th from the back, so the total = 13 + 8 − 1 = 20. (B cannot be ahead of A, since C would then be 1st and B would have no place.)
Answer: 20
60-Second Revision
- Total = left + right − 1.
- After an interchange, a person's new place is the other's old place.
- Check for overlap before counting people between.
- Class total = passed (r + s − 1) + failed + absent.