Ranking and Order Questions: Rank Formula

📑 On this page

⚡ The 20-second answer

Ordering questions come in three kinds: comparison chains (more than, less than), positions (from the front, from the back, between) and logical sequence (which step comes first). Put everything on one line facing one way, fix the definite facts first, and remember front + back − 1 = total. The trap: a chain with a gap has no single answer.

🎬 The 30-second story

The canteen queue

“I'm 9th from the front and 14th from the back. The samosas had better last.”

🍜

Meher

Meher, in the 1 pm canteen queue.

“9 plus 14. Twenty-three people. Easy.”

🧮

Aarav

Aarav, counting on his phone.

“I fried exactly 23 samosas and one is left over?”

🥟

Kabir

Kabir, at the counter.

“You counted Meher twice. Once from the front, once from the back. It's 22.”

📏

Zoya

Zoya, unimpressed.

Tara's verdict: One person counted from both ends shows up in both counts. Front + back − 1 = total: 9 + 14 − 1 = 22. Nearly every ranking question is this one line, rearranged.

How does CLAT word ordering and ranking questions?

CLAT 2018 asked one of each kind: a score chain, a queue position and a product sequence. Spot the family from the stem and each is a 30-second question.

The stem says	Family	First move
'Which team is in second place in the descending order of scores?' (2018 Q96)	Comparison chain	One chain, highest on the left
'What is my position in the queue?' (2018 Q104)	Position arithmetic	Put the fixed positions on a number line
'Arrange them in the most logical sequence' (2018 Q130)	Process sequence	Fix the first and last step
'How many people stand between A and B?'	Gap	Count both from the same end
'If they interchange places…'	Swap	The new spot is the other person's old spot

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🧭 Decision flow

Which ordering question is this?

❓ Does the stem compare people or things (more, less, taller, before)?

Yes →

Comparison chain. Write one chain in one direction.

No ↓

❓ Does it give positions from an end, or a total?

Yes →

Position arithmetic. Use front + back − 1 = total.

No ↓

❓ Are the items steps or stages of a process?

Yes →

Logical sequence. Anchor the ends, then test one pair.

No →

Probably a seating or grid puzzle: left, right and attributes.

How do you turn 'more than, less than' into one chain?

Never keep a list of clues. Keep one chain, biggest on the left, and hang each new clue onto a name already in it. First convert every clue to the same direction: 'A is shorter than B' is the same fact as B > A. 'Not as many as' means less than.

Rohan's message: Ishan is taller than Meher but shorter than Kabir. Tara is shorter than Meher. Flip 'shorter' and the chain writes itself.

🎚️ The scale

Rohan's height chain, tallest to shortest

← TallestShortest →

Kabir

taller than Ishan

Ishan

between Kabir and Meher

Meher

shorter than Ishan

Tara

shorter than Meher

What is the method for every ordering question?

1
Pick one direction
Highest, front or left goes at one end. Write everything that way.
2
Translate every clue
Flip 'less than' into 'more than'. Turn 'from the back' into 'from the front'.
3
Fix the definites first
Ends, given positions and fixed first or last steps go down before relative clues.
4
Check for gaps
Unlinked names or two possible cases? 'Cannot be determined' may be the answer.

What is the rank formula, and when does it give two answers?

🧮 The formula

The ranking identity

⬆️

Rank from the top

Meher: 9

⬇️

Rank from the bottom

Meher: 14

➖

− 1

she's counted twice

👥

Total

You know	You want	Formula
Rank from top t, from bottom b	Total	t + b − 1
Total N, rank p from one end	Rank from the other end	N − p + 1
Two positions p < q, same end	People between	q − p − 1
A pth from left, B qth from right, A left of B	People between	N − p − q
Positions p and q	Person exactly between	(p + q) ÷ 2, if p + q is even

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📌 Convert before you subtract

A is 7th from the left and B is 9th from the right in a row of 40. You can't subtract 7 from 9. Convert B: 40 − 9 + 1 = 32nd from the left. Between them: 32 − 7 − 1 = 24.

The overlap: when positions cross

If A is 7th from the left, B is 9th from the right and 3 people stand between them, the row has 19 people if A is left of B (7 + 3 + 9). But if they cross, so B is left of A, it has only 11 (7 + 9 − 3 − 2). Both rows are legal.

🪑 Seating plan

The 11-person row: B and A have crossed

Every clue checks out

✓P stands at the left end
✓A is 6th to the right of P, so 7th from the left
✓X stands at the right end
✓B is 8th to the left of X, so 9th from the right
✓Exactly 3 people stand between A and B

Same clues, a second legal row. Without 'A is ahead of B', the total isn't fixed.

⚠️ No 'ahead of'? Look for two answers

If the question never says who is nearer which end, test both cases. If both survive, 'cannot be determined' (or the option that lists both) is right. If one gives a total smaller than the people named, drop it.

How do you arrange steps in a logical sequence?

Process questions look like general knowledge but test two moves. Anchor the ends: what must come first and last? That usually kills two options. Test one pair: pick two steps where one clearly needs the other, and drop any option that reverses them.

🕒 Timeline

Kabir opens a cloud kitchen

🔍
1

Spot the demand

nothing starts without a need
📋
2

Plan the menu

you can't license a kitchen with no menu
📜
3

Get the food licence

required before selling anything
🧪
4

Trial run

test before customers see it
🚀
5

Launch on the apps

only after the trial
⭐
6

Collect reviews

needs real customers

💡 One clean pair beats a perfect order

You rarely need the full sequence. Once the ends are fixed, one 'X must come before Y' pair usually leaves a single option standing.

Can you solve these ordering questions in 40 seconds?

✍️ Worked example Warm-up ⏱ 30 sec

Five mock scores

Zoya scored more than Aarav but less than Meher. Kabir scored less than Aarav. Rohan scored more than Meher. Who is third highest?

1
Direction: highest on the left.
2
Clue 1: Meher > Zoya > Aarav.
3
Clue 2: Kabir hangs below Aarav. Clue 3: Rohan goes above Meher.
4
Chain: Rohan > Meher > Zoya > Aarav > Kabir. Every name linked, no gaps.

Answer: Zoya

⚡ The exam-hall shortcut

Write the first clue as a chain, then only extend its ends.

✍️ Worked example CLAT level ⏱ 40 sec

Meher's class rank

Meher is 14th from the top and 27th from the bottom of her class. Aarav is 9 ranks below Meher. What is Aarav's rank from the bottom?

1
Total = 14 + 27 − 1 = 40.
2
Aarav from the top = 14 + 9 = 23.
3
From the bottom = 40 − 23 + 1 = 18.

Answer: 18th from the bottom

⚡ The exam-hall shortcut

Skip the total: 9 ranks below Meher is 9 places nearer the bottom, so 27 − 9 = 18.

✍️ Worked example CLAT level ⏱ 60 sec

The fest quiz leaderboard

Six teams played the fest quiz final: Alpha, Beta, Gamma, Delta, Sigma and Omega. Gamma outscored Delta but trailed Beta. Alpha finished below Delta. Omega beat Beta. Sigma scored less than Gamma but more than Alpha. No two teams tied. The organisers announced only the top three on stage.

(i) Who came third? (ii) Who came fourth?

1
Clue 1: Beta > Gamma > Delta. Clue 2: Delta > Alpha. Clue 3: Omega > Beta.
2
Chain: Omega > Beta > Gamma > Delta > Alpha.
3
Sigma: below Gamma, above Alpha. It can sit above or below Delta.
4
So places 4 and 5 are Delta and Sigma in either order. Alpha is definitely last.

Answer: (i) Gamma. (ii) Cannot be determined: Delta or Sigma.

⚡ The exam-hall shortcut

When a name is squeezed between two others with another name already there, mark a gap. Ask only what the gap allows.

✍️ Worked example Tricky ⏱ 50 sec

Three between, two rows

In a row of students facing north, A is 7th from the left and B is 9th from the right. Exactly 3 students stand between A and B. How many students are in the row?

1
Case 1, A left of B: 7 + 3 + 9 = 19. Check: B is 11th from the left; 8, 9, 10 lie between. ✓
2
Case 2, B left of A: 7 + 9 − 3 − 2 = 11. B is 3rd from the left; 4, 5, 6 lie between. ✓
3
Nothing says who is nearer which end, so both rows stand.

Answer: 19 or 11, so 'cannot be determined' if both appear as options.

⚡ The exam-hall shortcut

No overlap: p + gap + q. Overlap: p + q − gap − 2.

How has CLAT asked ordering and ranking?

📝 Asked in CLAT 2018 · Q96 Comparison chain

In an archery match, Suresh's team got more scores than Mahesh's team but not as many as Yogesh's team. Yogesh's team got more scores than Mukesh's team. Mukesh's team got less score than Mahesh's team.

Which team is in second place in the descending order of scores?

AYogesh's team

BMukesh's team

CSuresh's team

DMahesh's team

Reveal answer + reasoning

Answer: C

Highest on the left. Clue 1 ('not as many as' = less than): Yogesh > Suresh > Mahesh. Clue 2 puts Mukesh somewhere below Yogesh. Clue 3 puts him below Mahesh, so last. Chain: Yogesh > Suresh > Mahesh > Mukesh. Answer C. Clue 2 was redundant once clue 3 arrived: a common CLAT padding move.

Why the others fail

A — First, not second.
B — Last.
D — Third.

📝 Asked in CLAT 2018 · Q104 Queue position

In a queue, I am the last person while my friend is seventh from the front. If the person exactly between me and my friend is on the 23rd position from the front, what is my position in the queue?

What is my position in the queue?

A37

B36

C38

D39

Reveal answer + reasoning

Answer: D

From my friend (7th) to the middle person (23rd) is 16 places. The middle person is equally far from me, so I am 16 further: 23 + 16 = 39. Check: (7 + 39) ÷ 2 = 23 ✓. Answer D.

Why the others fail

A — (7 + 37) ÷ 2 = 22, not 23.
B — (7 + 36) ÷ 2 = 21.5: there's no single middle person.
C — (7 + 38) ÷ 2 = 22.5: again no exact middle.

📝 Asked in CLAT 2018 · Q130 Logical sequence

Directions: Examine the following expressions/activities/processes, and arrange them in the most logical sequence. 1. Design, 2. Need, 3. Launching, 4. Research, 5. Testing, 6. Identify

Choose the most logical sequence.

A4, 1, 6, 2, 3, 5

B2, 6, 4, 1, 5, 3

C3, 5, 4, 1, 6, 2

D2, 4, 1, 5, 6, 3

Reveal answer + reasoning

Answer: B

Anchor the ends: a product begins with a Need (2) and ends with Launching (3). Only B and D do. One pair settles it: you identify the need before you research and design, but D puts Identify after Testing. Need → Identify → Research → Design → Testing → Launching. Answer B.

Why the others fail

A — Starts with research before there's a need, and launches before testing.
C — Starts with the launch.
D — Identifies the need only after the product is tested.

What do most students get wrong about ranking?

💥 Myth vs fact

Myth vs fact: ordering and ranking

🙅 Myth

Rank from the top + rank from the bottom = total.

Tap to bust it →

✅ Fact

Minus one. The person is counted in both.

🙅 Myth

Every ordering question has exactly one answer.

Tap to bust it →

✅ Fact

Chains leave gaps and rows can cross. 'Cannot be determined' is often the right option.

🙅 Myth

Someone always stands exactly between two people.

Tap to bust it →

✅ Fact

Only if p + q is even. That's how 2018 Q104's 36 and 38 die.

🙅 Myth

Sequence questions test business knowledge.

Tap to bust it →

✅ Fact

They test two anchors and one pair. Common sense, not a textbook.

Can you rank these five?

🎯 Quick quiz

Ordering and ranking quiz

0 / 5

Q1. P is taller than Q but shorter than R. S is shorter than Q. T is taller than R. Who is the shortest?

Q2. In a row of 45 students, Kabir is 17th from the left. What is his position from the right?

Q3. In a queue of 32, Aarav is 10th from the front and Zoya is 12th from the back. How many people stand between them?

After the hostel's Sunday mock, six friends compared scores. Meher scored more than Ishan but less than Zoya. Aarav scored more than Zoya. Kabir scored less than Meher but more than Rohan. Ishan did not score the lowest. No two friends scored the same, and nobody else took the mock that day. Meher posted the results on the group chat.

Q4. Which of the following must be true?

At the NLU counselling hall, candidates queue at the document counter. Kabir is 10th from the front. Zoya, who came with him, is 9th from the back. Zoya wants to stand near the fan, so the two swap places. After the swap, Kabir finds that he is 15th from the front. Nobody else joins or leaves the queue while this happens.

Q5. How many candidates are in the queue?

🎯 Ordering and ranking in a nutshell

One line, one direction. Flip 'less than' before you write.
Total = top + bottom − 1. Other end = N − p + 1.
Between two people: convert both to the same end, then q − p − 1.
An exact middle exists only when p + q is even.
No 'ahead of'? Test both cases.
Sequences: anchor both ends, then test one pair.

📎 Cheat sheet

'More than / less than / not as many as' → comparison chain → one chain, biggest on the left.
'From the front / back / left / right' → position arithmetic → convert to one end.
'Exactly between' → midpoint → (p + q) ÷ 2.
'Interchange places' → swap → new spot = partner's old spot.
'Most logical sequence' → process order → anchor first and last, test one pair.

Frequently asked questions

What is the formula for rank from the top and the bottom?

Rank from the top plus rank from the bottom, minus one, equals the total. The minus one is the person being counted, who appears in both counts. Someone 14th from the top and 27th from the bottom is in a class of 40, and rank from the other end is always total − rank + 1.

How do you find how many people stand between two people in a row?

Convert both positions to the same end first. If A is 7th from the left and B is 9th from the right in a row of 40, B is 32nd from the left, so 32 − 7 − 1 = 24 people stand between them. If the total is not given, check whether the two positions could overlap.

How do you solve 'more than, less than' ordering questions?

Turn every clue into the same direction, so 'A is shorter than B' becomes B taller than A. Write the first clue as one chain, biggest on the left, and hang each later clue on a name already in it. Before answering, check that every name is linked; a gap means 'cannot be determined'.

How do you arrange steps in the most logical sequence?

Fix the ends first: what must happen before anything else, and what can only happen last. That usually removes two options. Then pick one pair of steps where one clearly depends on the other and drop any option that reverses them. You rarely need to check the full order.