In this guide
Ranking questions are about positions: in a row, in a queue, in a class list, or in a line-up by height or weight. They look like arithmetic, but they are really about counting one person correctly. Almost every wrong answer in this topic is off by exactly one.
This guide gives you three formulas, a simple line diagram to back them up, the common question types, and a practice set. Once the formulas are in your fingers, most ranking questions take under 40 seconds.
The three formulas
| You know | You want | Formula |
|---|---|---|
| Position from both ends | Total people | Total = left position + right position − 1 |
| Total and position from one end | Position from the other end | Other end = total − position + 1 |
| Two positions from the same end | People between them | Between = bigger − smaller − 1 |
Why the "− 1" in the first formula? Because the person is counted twice, once from each end. Suppose a person is 3rd from the left and 3rd from the right. The row is: two people, then the person, then two people. That is 5, which is 3 + 3 − 1.
When to draw a line
The formulas cover the standard questions. For anything unusual, draw a short line, mark the ends as L and R (or Top and Bottom), and put each person on it. A quick drawing is the safest way to handle:
- "There are 4 people between A and B" questions, where you need the total.
- Swap questions, where two people change places.
- Questions with two people counted from different ends.
Comparison chains
Some questions compare people: "A is taller than B. C is taller than A." Write each statement with >, then join them into one chain.
- A > B and C > A give C > A > B.
- If two people are never linked by a statement, you cannot compare them. The answer may be "cannot be determined".
Worked examples
Example 1 (total): A student is 9th from the top and 16th from the bottom. How many students are in the class?
- Total = 9 + 16 − 1 = 24.
Example 2 (other end): In a row of 30 people, someone is 12th from the left. What is their position from the right?
- 30 − 12 + 1 = 19th from the right.
Example 3 (between): In a queue, two people are 5th and 14th from the front. How many people are between them?
- 14 − 5 − 1 = 8. They are the people in places 6 to 13.
Example 4 (people between, different ends): In a row, A is 8th from the left and B is 10th from the right. There are 4 people between them, and A is to the left of B. How many people are in the row?
- A is in place 8. The 4 people between take places 9 to 12. B is in place 13.
- B is 10th from the right, so total = 13 + 10 − 1 = 22.
- Quick check: 8 (up to A) + 4 (between) + 10 (from B to the right end) = 22.
Example 5 (swap): In a row, A is 10th from the left and B is 12th from the right. They swap places, and A becomes 18th from the left. How many people are in the row?
- After the swap, A sits in B's old seat. So B's old seat is 18th from the left.
- That seat was also 12th from the right (B's position before the swap).
- Total = 18 + 12 − 1 = 29.
Example 6 (comparison): A is taller than B. C is taller than A. B is taller than D. Who is the tallest, and who is second shortest?
- Chain: C > A > B > D.
- Tallest: C. Second shortest: B.
Common mistakes
- Forgetting the "− 1" in the total formula.
- Using the "between" formula for positions taken from different ends. Draw a line instead.
- In swap questions, forgetting whose position moved. The new position always belongs to the old seat of the other person.
- In "4 people between" questions, forgetting to check whether A is left or right of B. If the question does not say, there may be two answers.
- Assuming an order between two people who were never compared.
Practice set
- A student is 15th from the top and 20th from the bottom. How many students are there?
- In a row of 50, someone is 18th from the right. What is their position from the left?
- P is shorter than Q. R is shorter than P. Q is shorter than S. Who is the tallest?
- In a queue, two people are 7th and 20th from the front. How many are between them?
- X is 7th from the left and Y is 9th from the right. They swap places, and X becomes 15th from the left. How many people are in the row?
- In a row, A is 6th from the left and B is 7th from the right. There are 3 people between them, and A is to the left of B. How many people are in the row?
- Of five friends, P is heavier than Q but lighter than R. S is heavier than R. T is lighter than Q. Who is the lightest, and who is the second heaviest?
- A is taller than B. A is taller than C. Who is the shortest?
Answers:
- 34. 15 + 20 − 1.
- 33rd. 50 − 18 + 1.
- S. Chain: S > Q > P > R.
- 12. 20 − 7 − 1.
- 23. X is now in Y's old seat, which is 15th from the left and 9th from the right: 15 + 9 − 1.
- 16. A is in place 6, the 3 people take places 7 to 9, and B is in place 10. Total = 10 + 7 − 1 = 16.
- T is the lightest; R is the second heaviest. Chain: S > R > P > Q > T.
- Cannot be determined. Both B and C are shorter than A, but B and C are never compared.
What to do next
- Write the three formulas on a card and say where the "− 1" comes from.
- Solve 10 ranking questions a day for a week. Draw a line for every swap or "people between" question.
- Keep one "cannot be determined" example in your notes, so you remember that option exists.
- Next, move on to seating arrangement and puzzles, which build on the same line diagram. For a refresher on the direction words, see direction sense.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
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