← General Intelligence & Reasoning · DSSSB JE Civil

Chapter 5 of 10

Ranking & Seating Arrangement

In the DSSSB JE Civil syllabus under General Intelligence & Reasoning · 2 parts

Order & Ranking · Seating Arrangement

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📑 Contents (14 sections)

Part 1 of 2

Order & Ranking

Last reviewed 22 Sept 2026 · 5 min read

The one formula

FormulaRank and total

For a single line of $n$ people, where a person is $a$ th from one end and $b$ th from the other:

n = a + b - 1

The $- 1$ is because that person is counted from both ends. Rearranged, $a = n - b + 1$ .

Everything in this chapter is that formula, applied carefully.

Counting between two people

If two people are at positions $p$ and $q$ from the same end, the number between them is $∣ p - q ∣ - 1$ , and the number from one to the other inclusive is $∣ p - q ∣ + 1$ .

Exam TipRead the question's own words

"How many are between A and B" excludes both. "How many from A to B" includes both. One word changes the answer by two.

When the counts overlap

If a class has $n$ students and someone is $a$ th from the top and $b$ th from the bottom with $a + b > n + 1$ , then $a + b - n$ people have been counted twice — this is the standard "overlap" question, and the two positions describe different lines or a ranking with ties stated in the question.

Conversely, if $a + b < n + 1$ , there are $n - (a + b)$ people who are neither.

Comparison puzzles

"A is taller than B, C is shorter than B, D is taller than A" — draw a single line, tallest at the left, and place each name as it arrives. Use > between names and never keep two half-finished lines. The questions asked are: who is tallest, who is shortest, who is in the middle, and which statement cannot be determined.

Cannot be determined is a real answer here: if the puzzle never compares C with D, no ordering between them may be claimed.

Interchanged positions

When two people exchange places, everyone else stays put. If A was 7th from the left and after exchanging with B becomes 11th from the left, then B was 11th; and if the question also gives A's new rank from the right, the total follows from the formula.

Worked examples

Worked ExampleExample 1 — the total

In a row, Ram is 7th from the left and 12th from the right. How many are in the row?

Solution. $7 + 12 - 1 =$ 18.

Worked ExampleExample 2 — the other rank

In a class of 40, Sita is 15th from the top. What is her rank from the bottom?

Solution. $40 - 15 + 1 =$ 26th.

Worked ExampleExample 3 — between

In a queue, A is 9th from the front and B is 17th from the front. How many stand between them?

Solution. $17 - 9 - 1 =$ 7.

Worked ExampleExample 4 — from both ends, with a gap

In a row of 25, P is 8th from the left and Q is 6th from the right. How many are between them?

Solution. Q's position from the left is $25 - 6 + 1 = 20$ → between $= 20 - 8 - 1 =$ 11.

Worked ExampleExample 5 — overlap

In a class, a boy is 10th from the top and 25th from the bottom, and there are 30 students. How many have been counted twice?

Solution. $10 + 25 - 1 = 34$ against 30, so 4 students are counted in both lists.

Worked ExampleExample 6 — neither

In a row of 30, A is 8th from the left and B is 9th from the right. How many are neither A, nor B, nor between them?

Solution. B from the left is $30 - 9 + 1 = 22$ ; between them $= 22 - 8 - 1 = 13$ . Counting A and B, the block is 15 → 15 others are outside it.

Worked ExampleExample 7 — interchange

In a row, A is 11th from the left and B is 9th from the right. They exchange places; now A is 17th from the left. How many are in the row?

Solution. After the exchange A stands where B stood, so B was 17th from the left and also 9th from the right → $17 + 9 - 1 =$ 25.

Worked ExampleExample 8 — a comparison line

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

Solution. $C > A > B > D$ → tallest C, shortest D.

Worked ExampleExample 9 — what cannot be decided

P is heavier than Q. R is heavier than S. Q is heavier than S. Who is the lightest?

Solution. $P > Q > S$ and $R > S$ , so S is lighter than P, Q and R → S. But the order of R against P and Q cannot be determined.

Worked ExampleExample 10 — ranks in two subjects

In a class of 45, Anil ranks 12th in mathematics and 20th from the bottom in science. These are different lines — what can be said about his overall rank?

Solution. Nothing — ranks in two different orderings cannot be combined. The question tests whether the formula is applied blindly.

Part 2 of 2

Seating Arrangement

Last reviewed 22 Sept 2026 · 6 min read

Work the clues in the right order

The arrangement is found by the order in which clues are used, not by cleverness:

Fixed positions — "P sits at the extreme left", "Q is third from the right".
Blocks — "R sits immediately to the left of S": treat RS as one piece and slide it along.
Relative clues — "T sits between U and V" (which may be either way round).
Negative clues last — "W does not sit at either end" eliminates, and elimination is only useful once there is something to eliminate.

Exam TipTwo diagrams beat one rubbing-out

When a clue allows two placements, draw both and carry them forward. Most puzzles kill one of them within two clues, and the person who rubbed out has to start again.

Linear arrangements

A single row of 6 to 8 people, all facing the same way (usually north). Then:

If all face north, your left is their left as drawn — the leftmost seat is position 1.
If all face south, left and right are reversed with respect to the paper.

Two rows facing each other: row 1 faces south, row 2 faces north; the person opposite is directly across. Then P's "right" in row 1 sits across from someone on Q's "left" in row 2 — mark the facing arrow on each row before placing anybody.

Circular arrangements

RememberThe rule that decides every circular puzzle

Facing the centre: clockwise is to a person's left, anticlockwise is to their right. Facing outward: the opposite — clockwise is to their right.

For $n$ people evenly spaced, the person opposite someone is $n /2$ places away (only when $n$ is even). In a circle, "third to the left of X" is counted going round in X's left direction, skipping two seats.

Square and rectangular tables

Common form: eight people, four at the corners and four at the middles of the sides; corner-sitters face the centre and middle-sitters face outward, or the reverse. The facing rule above then applies person by person, not to the whole table — which is exactly what the question is testing.

Reading the clue words

Clue	Means
"Immediately to the left of"	adjacent, no one between
"To the left of"	anywhere on that side
"Third to the left of"	exactly two people in between
"Between A and B"	either order unless stated
"Exactly between"	equidistant from both
"Not adjacent to"	at least one seat apart

Worked examples

Worked ExampleExample 1 — a simple row

Six friends A to F sit in a row facing north. C is at the extreme right. A is second from the left. B is immediately to the right of A. D is not at either end. Where does B sit?

Solution. Positions 1–6 from the left: A is 2, so B is 3, and C is 6. B sits third from the left.

Worked ExampleExample 2 — a block that can slide

In a row of five seats, P and Q sit together, and R sits at one end. How many arrangements place PQ in that order with R at the left end?

Solution. With R fixed at seat 1, the block PQ may occupy seats 2-3, 3-4 or 4-5 → 3 placements (the remaining two people fill the rest in $2! = 2$ ways each, giving 6 full arrangements).

Worked ExampleExample 3 — facing the centre

Five people sit round a circle facing the centre. B is to the immediate left of A. Who is clockwise from A?

Solution. Facing the centre, clockwise is towards a person's left → B.

Worked ExampleExample 4 — facing outward

Six people sit round a circle facing outward. If X is third to the left of Y, how many people sit between them going clockwise from Y?

Solution. Facing outward, left is anticlockwise, so X is three places anticlockwise from Y — that is three places clockwise the other way round the six-seat circle, leaving two people between them clockwise from Y.

Worked ExampleExample 5 — opposite seats

Eight people sit evenly round a circular table. Who sits opposite the person who is third to the right of P?

Solution. Third to the right of P is a definite seat; opposite is $8/2 =$ four seats further on, which is the person third to the left of P.

Worked ExampleExample 6 — two rows

Six people sit in two rows of three facing each other. A, B, C face south; D, E, F face north. A is opposite E, and B sits to the immediate right of A. Who is opposite B?

Solution. A faces south, so A's right is towards the paper's left. B is there, and the person opposite B is the one to E's left as E faces north — that is D or F, decided by the next clue. Without it, it cannot be determined.

Worked ExampleExample 7 — counting places

In a circle of ten facing the centre, if M is fourth to the left of N, how many sit between them on the other side?

Solution. Four places one way leaves $10 - 4 = 6$ places the other way, so five people sit between them going the long way round.

Worked ExampleExample 8 — negatives

Five students sit in a row. P is not at either end, Q is at the extreme left, and R sits immediately to the right of P. If S is at the extreme right, where does T sit?

Solution. Q is 1 and S is 5. P cannot be 5, and R follows P, so P is 2, 3 or 4 with R next. If P=2, R=3, T=4. If P=3, R=4, T=2. Both survive, so T sits at position 2 or 4 — a second clue is needed to fix it.

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