Order and ranking for RRB NTPC: formulas, swaps, comparisons, practice

Order and ranking questions are about positions: in a row, a queue or a class list. A second type compares people by height, weight or marks and asks who comes first or last. Both are medium-speed questions, usually 30–50 seconds, and both reward a quick line diagram over mental juggling.

Nearly every ranking question rests on one idea: when you count a person's position from both ends, that person is counted twice. Once you see why the formula has a "− 1", the rest follows.

The three formulas

• Total = position from one end + position from the other end − 1
• Position from the other end = total − given position + 1
• People between positions p and q (both counted from the same end, q larger) = q − p − 1

Why the − 1 in the first formula? If someone is 3rd from the left and 3rd from the right, there are two people on each side plus the person, so 5 in all. 3 + 3 counts that person twice; 3 + 3 − 1 = 5.

A method

1. Draw a line and mark the two ends (left and right, or top and bottom).
2. Convert every position to the same end. If one person is given from the left and another from the right, use the second formula to bring both to the left.
3. Place people on the line and read off the answer.
4. For comparisons, write a chain with the largest on the left: C > A > B > D.

Worked questions

Q1. A student is 7th from the top and 12th from the bottom of a class. How many students are in the class?

7 + 12 − 1 = 18.

Q2. In a row of 25 people, B is 10th from the left. What is B's position from the right?

25 − 10 + 1 = 16th.

Q3. In a queue, P is 8th from the front and Q is 15th from the front. How many people stand between them?

15 − 8 − 1 = 6.

Q4. In a row of 40 people, P is 10th from the left and Q is 12th from the right. How many people are between them?

Bring Q to the left end: 40 − 12 + 1 = 29th from the left. Between 10th and 29th: 29 − 10 − 1 = 18.

Q5. In a row, A is 12th from the left and B is 15th from the right. They swap places, and A becomes 20th from the left. How many people are in the row?

After the swap, A sits in B's old seat, so that seat is 20th from the left and 15th from the right. Total = 20 + 15 − 1 = 34. As a check, B is now in A's old seat, 12th from the left.

Q6. In a row, P is 15th from the left and Q is 18th from the right. There are 5 people between them. What is the minimum number of people in the row?

There are two cases.

• Q to the right of P. Count from the left: 15 for P, 5 between, then Q, then 17 more after Q. Total = 15 + 5 + 18 = 38.
• Q to the left of P. Q is 6 places left of P, so Q is 9th from the left. Q is also 18th from the right, so total = 9 + 18 − 1 = 26. Check: between the 9th and 15th seats are seats 10 to 14, which is 5 people.

The minimum is 26.

Q7. A is taller than B. C is taller than A. D is shorter than B. Who is the tallest, and who is the shortest?

Chain: C > A > B > D. C is the tallest and D the shortest.

Comparison chains

Write every "taller than" or "heavier than" statement as a link in one chain, largest on the left. Then check whether every person has been linked.

If two people are never compared directly or through someone else, their order is unknown. For example, if A > B and A > C, you know A is the tallest of the three, but you cannot tell whether B or C is shorter. The correct answer then is "cannot be determined".

Common mistakes

• Forgetting the − 1 in the total formula.
• Mixing ends. Convert every position to one end before comparing.
• Swapping the wrong people in interchange questions. The person who moves takes on the other person's old position from both ends.
• Stopping at one case in "minimum" or "maximum" questions.
• Forcing an answer when a comparison chain has a gap.

Practice set

1. A student is 11th from the top and 20th from the bottom. How many students are in the class?
2. In a row of 40, someone is 13th from the right. What is their position from the left?
3. P is taller than Q. R is taller than P. S is shorter than Q. Who is the shortest?
4. In a queue, two people are 6th and 17th from the front. How many people stand between them?
5. X is 9th from the left and Y is 11th from the right. They swap places, and X becomes 16th from the left. How many people are in the row?
6. In a row of 35, M is 14th from the left and N is 9th from the right. How many people are between them?
7. A is heavier than B and C. D is lighter than B. Who is the lightest?
8. In a row, J is 10th from the left and K is 12th from the right, with 4 people between them. What is the minimum number of people in the row?

Answers:

1. 30. 11 + 20 − 1.
2. 28th. 40 − 13 + 1.
3. S. R > P > Q > S.
4. 10. 17 − 6 − 1.
5. 26. X now sits in Y's old seat: 16th from the left and 11th from the right; 16 + 11 − 1.
6. 12. N is 35 − 9 + 1 = 27th from the left; 27 − 14 − 1 = 12.
7. Cannot be determined. A > B > D and A > C, but C is never compared with B or D.
8. 16. If K is to the left of J, K is 5th from the left (4 people in seats 6 to 9), and 5 + 12 − 1 = 16. The other case gives 10 + 4 + 12 = 26.

What to do next

• Memorise the three formulas and the reason for the − 1.
• Solve ten interchange questions and ten "minimum number" questions; these are where marks are lost.
• Draw a line diagram for every question, even simple ones, for one week.
• Next, try seating arrangement, which builds on positions in a row, and revise direction and distance.