Order and ranking for IBPS Clerk

Ranking questions ask about positions in a row or a queue, or ranks in a class. They look like counting, and they are, but the formula has a "+1" in it that catches people every exam. Learn why the +1 is there and the whole topic becomes arithmetic.

In the prelims you will see these as quick one-liners and as comparison chains ("A is taller than B…"). The same reasoning drives the tallest-to-shortest and heaviest-to-lightest clues inside the mains puzzles, so the time you spend here pays off twice.

The key formula

Position from the left + position from the right = total + 1

Why +1? Because the person you are describing is counted twice, once from each end. In a row of 5, the middle person is 3rd from the left and 3rd from the right: 3 + 3 = 6, which is 5 + 1.

The same formula works for rank from the top and rank from the bottom, and for position from the front and back of a queue.

Worked examples

Example 1. In a row of 40 students, A is 12th from the left. What is A's position from the right?

1. Right = total + 1 − left = 40 + 1 − 12.
2. 29th from the right.

Example 2. A is 15th from the left and 20th from the right. How many people are in the row?

1. Total = 15 + 20 − 1.
2. 34.

Example 3 (people between). In a row of 45, A is 12th from the left and B is 15th from the right. How many people stand between them?

1. Convert B to the same end: 45 + 1 − 15 = 31st from the left.
2. A is 12th and B is 31st from the left. Between them: 31 − 12 − 1 = 18.
3. 18.

Example 4 (overlap). In a row of 30, P is 20th from the left and Q is 18th from the right. How many people stand between them?

1. The quick guess, 30 − 20 − 18 = −8, is negative. That tells you the two counts overlap.
2. Convert Q: 30 + 1 − 18 = 13th from the left.
3. Q is 13th and P is 20th from the left. Between them: 20 − 13 − 1 = 6.
4. 6.

Example 5 (interchange). In a row, A is 10th from the left and B is 15th from the right. They swap places, and A is now 18th from the left. How many people are in the row? What is B's new position from the right?

1. After the swap, A stands in B's old place. That place is 18th from the left and 15th from the right.
2. Total = 18 + 15 − 1 = 32.
3. B now stands in A's old place, 10th from the left. From the right: 32 + 1 − 10 = 23.
4. 32 people; B is 23rd from the right.

Example 6 (minimum number). In a queue, A is 7th from the front and B is 5th from the back. There are exactly 3 people between A and B. What is the minimum number of people in the queue?

1. Case 1, A ahead of B: B is 7 + 4 = 11th from the front. Total = 11 + 5 − 1 = 15.
2. Case 2, B ahead of A: B is 7 − 4 = 3rd from the front. Total = 3 + 5 − 1 = 7.
3. Check case 2: in a queue of 7, B at 3rd is 5th from the back, A is 7th, and 4th, 5th and 6th stand between them. It works.
4. Minimum 7. (Case 1 gives 15, the other possible answer.)

Comparison chains

These questions compare heights, weights, marks or ages. Join every clue into one chain, largest on the left.

Example 7. Among five friends, P is taller than Q but shorter than R. S is taller than R. T is shorter than Q. Who is the third tallest?

1. P is taller than Q and shorter than R: R > P > Q.
2. S is taller than R: S > R > P > Q.
3. T is shorter than Q: S > R > P > Q > T.
4. P is the third tallest.

If the clues do not link everyone into one chain, say so. When two people are never compared, a question like "who is second tallest?" may have no single answer.

Common mistakes

• Dropping the +1 or the −1. Say the reason to yourself: "the person is counted twice."
• Subtracting positions counted from different ends. Convert one first.
• Taking the first case in a "minimum" or "maximum" question without checking the other order.
• In interchange questions, attaching the new position to the wrong person. The person who moved takes the other person's seat, and that seat is the one known from both ends.
• In comparison chains, treating "not taller than" as "shorter than". It allows equal heights.

Practice

Aim for six minutes.

1. In a row of 30, B is 7th from the right. What is B's position from the left?
2. A student is 11th from the top and 11th from the bottom of a class. How many students are in the class?
3. P is heavier than Q. R is heavier than P. S is lighter than Q. Who is the heaviest and who is the lightest?
4. In a class of 50, M ranks 14th from the top. N is 9 ranks below M. What is N's rank from the bottom?
5. In a row, X is 9th from the left and Y is 12th from the right. Y is to the right of X, and exactly 4 people stand between them. How many people are in the row?
6. In a row, C is 16th from the left and D is 11th from the right. They swap places, and C is now 20th from the left. What is D's new position from the right?
7. Of five boxes, J is heavier than K. L is lighter than K but heavier than M. N is heavier than J. Which box is the second heaviest?
8. In a row of 40, how many people stand between the person 10th from the left and the person 10th from the right?

Answers:

1. 24th. 30 + 1 − 7 = 24.
2. 21. 11 + 11 − 1 = 21.
3. R heaviest, S lightest. The chain is R > P > Q > S.
4. 28th. N is 14 + 9 = 23rd from the top. From the bottom: 50 + 1 − 23 = 28.
5. 25. Y is 9 + 5 = 14th from the left. Total = 14 + 12 − 1 = 25.
6. 15th. C now stands in D's old seat: 20th from the left and 11th from the right, so the row has 30. D now stands in C's old seat, 16th from the left: 30 + 1 − 16 = 15th from the right.
7. J. The chain is N > J > K > L > M.
8. 20. 10th from the right is 31st from the left. Between: 31 − 10 − 1 = 20.

What to do next

• Write the four formulas in the table from memory, with the reason for each +1 or −1.
• Solve 10 ranking questions a day for a week, including two overlap and two interchange questions.
• Practise comparison chains inside full puzzles, since that is where they cost the most time.
• Continue with direction sense and data sufficiency, which often uses ranking statements.