In this guide
Direction questions test one thing: can you keep track of where someone is and which way they are facing while they walk and turn? The arithmetic is simple. The errors come from turning the wrong way in your head, usually on the third or fourth turn.
The cure is to draw every path, however short, and to track two things separately: position and facing. A left turn changes the facing, not the position. The walk changes the position, not the facing.
How it is asked
- Final distance and direction: "How far is the person from the start, and in which direction?"
- Final facing: "After these turns, which way is the person facing?"
- Relative position: "Town X is 12 km north of Y, and Z is 5 km west of Y. How far is Z from X?"
- Angle turns: "Facing north, a person turns 135° clockwise…"
- Shadows: "In the morning, a person's shadow falls to their right. Which way are they facing?"
The compass and turns
North is at the top of your sketch, south at the bottom, east on the right and west on the left. North-east, south-east, south-west and north-west lie halfway between.
| Facing | A right turn faces | A left turn faces | An about-turn faces |
|---|---|---|---|
| North | East | West | South |
| East | South | North | West |
| South | West | East | North |
| West | North | South | East |
A right turn is 90° clockwise and a left turn is 90° anticlockwise. Two right turns, or two left turns, reverse the direction.
The coordinate method
Put the start at (0, 0). East is +x, west is −x, north is +y and south is −y.
- Write the current facing next to your sketch.
- For each turn, update the facing using the table above.
- For each walk, add the distance to x or y.
- At the end, the straight-line distance is √(x² + y²).
- The direction comes from the signs: +x and +y is north-east, −x and +y is north-west, and so on. If x = 0 or y = 0, it is a pure direction.
Why coordinates help: a sketch shows the shape; coordinates stop you from misreading it. After four or five legs, the numbers are more reliable than your drawing.
The common right triangles make the square roots easy: 3–4–5, 6–8–10, 5–12–13, 8–15–17 and 9–12–15.
Angles and shadows
For angle turns, work in 45° steps. Clockwise from north: 45° is north-east, 90° east, 135° south-east, 180° south, 225° south-west, 270° west, 315° north-west.
For shadows, the sun rises in the east and sets in the west, and a shadow falls away from the sun.
- Morning: the sun is in the east, so shadows fall towards the west.
- Evening: the sun is in the west, so shadows fall towards the east.
- Noon: questions usually avoid noon, because the shadow is then short and its direction depends on the season and the place.
Then ask: if the shadow points west and falls to the person's right, which way must they face for west to be on their right? Facing south, west is on the right.
Six worked questions
Q1. A person walks 6 km east, turns left and walks 8 km, then turns left again and walks 12 km. How far are they from the start, and in which direction? (a) 10 km north-west (b) 10 km north-east (c) 14 km north-west (d) 26 km west
East 6: (6, 0). Left turn from east faces north; 8 km: (6, 8). Left turn from north faces west; 12 km: (−6, 8). Distance √(36 + 64) = 10. x is negative and y positive, so north-west. Answer: (a).
Q2. A person walks 4 km south, turns left and walks 3 km, turns left and walks 12 km, then turns right and walks 3 km. How far are they from the start? (a) 8 km (b) 10 km (c) 12 km (d) 13 km
South 4: (0, −4). Left from south faces east; 3 km: (3, −4). Left from east faces north; 12 km: (3, 8). Right from north faces east; 3 km: (6, 8). √(36 + 64) = 10, towards the north-east. Answer: (b) 10 km.
Q3. Facing west, a person turns right, then right again, then left. Which way are they facing? (a) North (b) South (c) East (d) West
West, right → north, right → east, left → north. Answer: (a) North.
Q4. Facing east, a person turns 90° anticlockwise, then 225° clockwise. Which way are they facing? (a) South-east (b) South-west (c) North-west (d) West
90° anticlockwise from east is north. From north, 180° clockwise is south and another 45° clockwise is south-west. Answer: (b) South-west.
Q5. In the morning, a person's shadow falls to their left. Which way are they facing? (a) North (b) South (c) East (d) West
In the morning the shadow points west. West is on your left when you face north. Answer: (a) North.
Q6. Town X is 12 km north of town Y. Town Z is 5 km west of Y. How far is Z from X, and in which direction? (a) 13 km south-west (b) 13 km north-west (c) 17 km south-west (d) 13 km south-east
With Y at (0, 0), X is at (0, 12) and Z at (−5, 0). From X to Z you go 5 west and 12 south: √(25 + 144) = 13, towards the south-west. Answer: (a).
Common traps
| Trap | Fix |
|---|---|
| Turning relative to the page | Use the facing table for every turn |
| Adding distances instead of using Pythagoras | Distance is √(x² + y²) |
| Answering the reverse direction | Check "from the start" or "from the person" |
| Mixing clockwise and anticlockwise | Right = clockwise; left = anticlockwise |
| Getting the shadow side wrong | Morning shadow west, evening shadow east |
Practice
- A person walks 5 km north, turns right and walks 3 km, then turns right and walks 5 km. How far and in which direction are they from the start? (a) 3 km east (b) 3 km west (c) 13 km east (d) 5 km south
- Facing south, a person turns left and then left again. Which way are they facing? (a) East (b) West (c) North (d) South
- A cyclist rides 8 km west and then 6 km south. What is the shortest distance from the start, and in which direction? (a) 14 km south-west (b) 10 km south-west (c) 10 km north-west (d) 2 km south
- Facing east, a person turns 90° anticlockwise and then 180°. Which way are they facing? (a) North (b) South (c) West (d) East
- In the morning, a boy's shadow falls to his right. Which way is he facing? (a) North (b) South (c) East (d) West
- A person walks 10 m south, turns right and walks 10 m, turns right and walks 10 m, then turns left and walks 5 m. Where are they relative to the start? (a) 5 m west (b) 15 m west (c) 15 m east (d) 10 m north
- Facing north, a person turns 135° clockwise and then 90° anticlockwise. Which way are they facing? (a) North-east (b) South-east (c) North-west (d) East
- At 3 o'clock, the minute hand of a clock points north. Which way does the hour hand point? (a) South (b) West (c) East (d) North-east
Answers:
- (a) 3 km east. (0, 5), then (3, 5), then facing south: (3, 0).
- (c) North. South, left → east, left → north.
- (b) 10 km south-west. (−8, −6): √(64 + 36) = 10.
- (b) South. East → north after 90° anticlockwise, then 180° → south.
- (b) South. The morning shadow points west, and west is on your right when you face south.
- (b) 15 m west. (0, −10); right from south faces west: (−10, −10); right from west faces north: (−10, 0); left from north faces west: (−15, 0).
- (a) North-east. 135° clockwise from north is south-east; 90° anticlockwise from south-east is north-east.
- (c) East. The minute hand at 12 points north, so the 3 on the dial is east, and the hour hand points at 3.
What to do next
- Draw every direction question for two weeks, writing the facing next to each leg.
- Learn the five right triangles above so the final distance takes seconds.
- Do ten shadow and angle-turn questions; they are few, but they trip people who never practised them.
- Next, try blood relations, which rewards the same draw-first habit, and ranking and order.
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 Staff Selection Commission website .
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