Direction and distance reasoning shows up in almost every SSC, Railway, Banking and TET paper, and it is one of the few reasoning topics where a single method solves nearly every question. This guide covers the origin-coordinate method, the clockwise right-turn rule and the Pythagoras shortcut, plus shadow-based and multi-person questions that many study pages leave out. Each trick comes with a fully worked example you can follow on rough paper.
Table of Contents
How Direction and Distance Reasoning Works
Every question in direction and distance reasoning describes a path. Someone starts at a point, walks some distance, turns, walks again, and the examiner asks one of three things: the final direction the person is facing, the straight-line distance from the starting point, or the direction of the end point from the start.
Before any trick works, you need a fixed map in your head. Exams follow the standard convention used on paper maps: North at the top, South at the bottom, East on the right and West on the left. The four in-between directions are North-East, North-West, South-East and South-West.
| Direction | Position on paper | Opposite direction | Angle from North (clockwise) |
|---|---|---|---|
| North (N) | Top | South | 0° |
| North-East (NE) | Top-right | South-West | 45° |
| East (E) | Right | West | 90° |
| South-East (SE) | Bottom-right | North-West | 135° |
| South (S) | Bottom | North | 180° |
| South-West (SW) | Bottom-left | North-East | 225° |
| West (W) | Left | East | 270° |
| North-West (NW) | Top-left | South-East | 315° |
Note the difference between distance travelled and displacement. If you walk 5 m north and 5 m back south, you have travelled 10 m but you are 0 m from the start. When a question asks how far someone is from the starting point, it always means displacement, the straight line between start and finish.
Read the last line of the question first. Knowing whether it wants a facing direction, a distance or a relative position tells you which details matter and which you can skip.
What Does Turning Right Mean in Direction Questions?
A right turn is always a 90° turn in the clockwise direction from wherever the person is currently facing. A left turn is 90° anticlockwise. This is the single rule that trips up most candidates, because they imagine turning right on the paper instead of turning right from the walker’s own point of view.
If a man walking south turns right, he does not move towards the right side of your page (East). From his own view, facing south, his right hand points West. Keep the clockwise rule in mind and you will not get this wrong.
| Currently facing | After right turn | After left turn | After about-turn (180°) |
|---|---|---|---|
| North | East | West | South |
| East | South | North | West |
| South | West | East | North |
| West | North | South | East |
Turns other than 90°
Some questions mention turns of 45°, 135° or 180°. Convert each turn into degrees on the clockwise scale shown in the first table. Clockwise turns add degrees, anticlockwise turns subtract them, and any result below 0° or above 360° is brought back into range by adding or subtracting 360°.
- Facing North, turn 45° clockwise: 0° + 45° = 45°, so the person faces North-East.
- Facing East, turn 135° anticlockwise: 90° − 135° = −45°, which equals 315°, so the person faces North-West.
- Facing South-West, turn 90° clockwise: 225° + 90° = 315°, so the person faces North-West.
The Origin-Coordinate Method, Step by Step
Drawing a rough diagram works for short paths, but long paths with five or six turns get messy. The origin-coordinate method replaces drawing with simple addition. Treat the starting point as (0, 0). Movement east adds to x, west subtracts from x, north adds to y and south subtracts from y.
- Write the starting point as (0, 0) and note the direction the person faces.
- For each instruction, first update the facing direction using the right-turn rule.
- Then add or subtract the distance from x or y.
- At the end, read the final point (x, y). Its signs tell you the direction from the start; its size gives the distance.
Solved example 1
Ravi walks 10 m north, turns right and walks 6 m, turns right again and walks 18 m, then turns left and walks 9 m. How far is he from the starting point, and in which direction?
| Step | Facing | Move | Position (x, y) |
|---|---|---|---|
| Start | North | – | (0, 0) |
| 1 | North | 10 m | (0, 10) |
| 2 | East (right of North) | 6 m | (6, 10) |
| 3 | South (right of East) | 18 m | (6, −8) |
| 4 | East (left of South) | 9 m | (15, −8) |
The final point is (15, −8). Positive x means east, negative y means south, so Ravi is south-east of his start. The distance is √(15² + 8²) = √(225 + 64) = √289 = 17 m.
No sketch was needed. On exam day, a quick table like this in the margin of your rough sheet takes well under a minute and leaves little room for error.
Reading the sign of the final point
- x positive, y positive: North-East of the start.
- x negative, y positive: North-West.
- x negative, y negative: South-West.
- x positive, y negative: South-East.
- x or y equal to zero: the person lies due north, south, east or west of the start.
How to Find the Shortest Distance
The shortest distance between the start and end point is the straight line joining them. Once you have the net east-west movement (x) and the net north-south movement (y), the answer is the hypotenuse of a right-angled triangle: distance = √(x² + y²).
Net out opposite moves first. If someone walks 12 m north and later 4 m south, the net north-south movement is 8 m north. Never add all the distances together; that gives the path length, which is a common trap option in the answer choices.
Memorise these Pythagorean triplets
Examiners usually choose numbers that give whole-number answers. If you recognise a Pythagorean triplet, you can skip the square root entirely.
| Net x | Net y | Shortest distance | Multiples to watch |
|---|---|---|---|
| 3 | 4 | 5 | 6-8-10, 9-12-15, 12-16-20 |
| 5 | 12 | 13 | 10-24-26 |
| 8 | 15 | 17 | 16-30-34 |
| 7 | 24 | 25 | 14-48-50 |
| 20 | 21 | 29 | – |
Solved example 2
A cyclist rides 7 km east, 20 km north, 17 km west and 4 km south. How far is she from the start? Net east-west: 7 − 17 = −10, so 10 km west. Net north-south: 20 − 4 = 16 km north. Distance = √(100 + 256) = √356, about 18.87 km, towards the north-west.
If an option reads 2√89 km, that is the same value in surd form (356 = 4 × 89), so always simplify before comparing with the choices.
When only one axis has movement left after netting, no formula is needed. For example, 10 m north, 8 m east, 10 m south leaves the person exactly 8 m east of the start.
The Shadow Rule in Direction Sense
Shadow questions are skipped by many candidates, yet they follow one fixed fact: a shadow always falls on the side opposite the sun. Since the sun rises in the east and sets in the west, the rule for exam questions is simple.
| Time of day | Sun is in the | Shadow falls towards |
|---|---|---|
| Morning (after sunrise) | East | West |
| Evening (before sunset) | West | East |
| Around noon | High in the sky | Very short; exams usually avoid this case |
The second half of the rule is about the person’s body. Once you know where the shadow points, combine it with front, back, left or right to find which way the person faces.
- Morning, shadow in front: the person faces West.
- Morning, shadow behind: faces East.
- Morning, shadow to the left: faces North (left of North is West).
- Morning, shadow to the right: faces South (right of South is West).
- Evening, shadow in front: faces East.
- Evening, shadow to the right: faces North (right of North is East).
Solved example 3
One morning after sunrise, Anil and Sunil stand facing each other. Anil’s shadow falls exactly to his right. Which direction is Sunil facing? In the morning, shadows fall west. Anil’s right hand points west, so Anil faces south. Sunil faces Anil, so Sunil faces north.
Solved example 4
In the evening, Meena walks towards her shadow, then turns left. Which way is she walking now? Evening shadows fall east, so she was walking east. A left turn from east is north.
Multi-Person and Relative Position Questions
Newer papers often describe the positions of several people or places and ask where one stands in relation to another. The origin-coordinate method handles these well, because you can give every person their own coordinates.
Solved example 5
P is 8 m east of Q. R is 6 m north of Q. S is 6 m north of P. Find the position of S with respect to R, and the distance between P and R.
- Place Q at (0, 0).
- P is 8 m east: P = (8, 0).
- R is 6 m north of Q: R = (0, 6).
- S is 6 m north of P: S = (8, 6).
S and R share the same y value, so S is 8 m east of R. For P and R, the gap is 8 m in x and 6 m in y, so the distance is 10 m (a 6-8-10 triplet). R lies north-west of P.
Read the reference point carefully
“Where is A with respect to B” means stand at B and look towards A. Subtract B’s coordinates from A’s: the signs of the result give the direction. Reversing this order flips the answer, for example North-East becomes South-West, and both usually appear in the options.
Some puzzles mix directions with family links, such as “A’s brother is standing north of A’s father”. Solve the relationship part first, then plot the positions. If those questions slow you down, practise blood relations reasoning separately so that half of the puzzle becomes automatic.
7 Tricks to Solve Direction and Distance Reasoning Fast
These are the methods that save the most time across SSC, RRB and banking papers. Practise each until it feels mechanical, and direction and distance reasoning becomes one of the quickest scoring areas of the reasoning section.
- Fix the map first. Draw a small N-E-S-W cross in the corner of your rough sheet before reading the question.
- Right means clockwise. Always turn from the walker’s current facing direction, never from the page.
- Use coordinates for three or more turns. A four-column table (step, facing, move, position) beats a sketch for long paths.
- Net out opposites. Combine all north and south moves into one figure, and all east and west moves into another, before calculating.
- Count net turns for facing-direction questions. Score each right turn as +90° and each left as −90°. Facing north, the turns R, R, L, R total +180°, so the final direction is south. Distances do not matter here.
- Spot the triplet. If the net figures are 5 and 12, or 8 and 15, write the answer without any calculation.
- Apply the shadow rule in two steps. First fix the shadow direction from the time of day, then use front, back, left or right to find the facing direction.
Common mistakes that cost marks
- Adding every distance instead of finding displacement.
- Turning right relative to the page rather than the person.
- Reading “A from B” as “B from A”.
- Forgetting that a left turn from south is east, not west.
- Answering the direction the person faces when the question asks for the direction from the start.
A good habit: after solving, glance at the options. If one option equals the total path length, it is almost certainly a trap built for candidates who skipped netting.
How Many Direction Questions Come in SSC CGL?
In the SSC CGL Tier 1 computer-based exam, General Intelligence and Reasoning carries 25 questions for 50 marks, out of 100 questions in total. SSC does not publish a topic-wise split, so any figure for one chapter is an estimate. Going by recent papers, direction sense usually accounts for roughly one to two questions per shift, sometimes merged into a puzzle.
That may sound small, but these are among the fastest marks in the paper. A well-practised candidate can solve a direction question in under a minute, freeing time for longer series and puzzle sets. Because 0.50 marks are deducted for each wrong answer in Tier 1, accuracy matters more than speed, which is another reason to rely on a fixed method instead of guesswork.
| Exam | Where direction sense appears | Approximate frequency |
|---|---|---|
| SSC CGL Tier 1 | General Intelligence and Reasoning | About 1-2 questions |
| SSC CHSL Tier 1 | General Intelligence | About 1-2 questions |
| RRB NTPC / Group D | General Intelligence and Reasoning | About 1-2 questions |
| Bank PO / Clerk prelims | Reasoning Ability (often as puzzles) | Varies; sometimes a set of 3-5 |
The frequencies above are approximate, based on recent papers. Always confirm the current exam scheme, dates and marking rules in the latest notice on the official Staff Selection Commission website, because patterns can change between cycles.
To build a complete reasoning toolkit, pair this chapter with coding-decoding practice, another topic that rewards a fixed method. If you are targeting the 12th-level exam, our SSC CHSL preparation guide shows how to fit direction and distance reasoning into a weekly study plan alongside quant and English.
Frequently Asked Questions
How do you solve direction and distance questions quickly?
Treat the starting point as (0, 0) and track every move as a change in x or y, turning clockwise for right and anticlockwise for left. Net out opposite moves, then use Pythagoras for the straight-line distance. For facing-direction questions, simply add +90° for each right turn and −90° for each left turn.
What is the shadow rule in direction sense?
A shadow always falls opposite the sun. In the morning the sun is in the east, so shadows fall west; in the evening the sun is in the west, so shadows fall east. Combine the shadow direction with front, back, left or right of the person to find which way they are facing.
How do you find the shortest distance in direction questions?
First calculate the net east-west movement and the net north-south movement by cancelling opposite moves. The shortest distance is the square root of the sum of their squares. Recognising triplets such as 3-4-5, 5-12-13 and 8-15-17 lets you skip the square root and answer within seconds.
What does turning right mean in direction reasoning?
Turning right means rotating 90° clockwise from the direction the person is currently facing, not towards the right side of the page. So a person facing north turns to east, facing east turns to south, facing south turns to west, and facing west turns to north.