Direction Sense
CSAT · Logical Reasoning
Introduction
Direction questions trace a person's walk through turns and distances. With a quick sketch on coordinates, both the final distance and the direction from the start become simple.
Key concepts
The compass
North is up, east right, south down, west left. Between them: north-east, south-east, south-west, north-west.
Turning
- Right turn = 90° clockwise; left turn = 90° anticlockwise.
- Facing north: right → east, left → west. Facing east: right → south, left → north. Facing south: right → west, left → east. Facing west: right → north, left → south.
- A turn of 45° goes to the intermediate direction.
Coordinates method
Write east and north as positive. Add each leg to x (east–west) or y (north–south). The final point (x, y) gives:
- distance from the start = √(x² + y²);
- direction from the start: north/south from the sign of y, east/west from the sign of x.
Shadows
In the morning the sun is in the east, so shadows fall to the west; in the evening they fall to the east. At noon in India there is a short shadow towards the north.
Direction 'of' and 'from'
'Where is A from B?' means stand at B and look towards A.
- Distance = √(x² + y²)
- Right = clockwise 90°; left = anticlockwise 90°
- Morning shadow → west; evening → east
Solved examples
Example 1
Meena walks 12 km south, then turns right and walks 6 km, then turns left and walks 4 km, then turns left and walks 6 km. In which direction is she now from her starting point?
(a) south-east (b) north-west (c) south (d) north
- Net displacement: 0 km (none east–west), 16 km south.
- So she is to the south of the start (she is facing east at the end, which does not matter).
Answer: (c) south
Example 2
Ravi walks 2 km west, then turns left and walks 4 km, then turns right and walks 3 km, then turns left and walks 4 km, then turns left and walks 5 km. How far is he from his starting point?
(a) 8 km (b) 9 km (c) 11 km (d) 10 km
- Track east–west and north–south separately (east and north positive).
- Net: 0 km and 8 km south.
- Distance = √(0² + 8²) = √64 = 8 km.
Answer: (a) 8 km
Example 3
Meena walks 3 km east, then turns right and walks 5 km, then turns right and walks 8 km, then turns right and walks 5 km. In which direction is she now from her starting point?
(a) south-west (b) west (c) south (d) east
- Net displacement: 5 km west, 0 km (none north–south).
- So she is to the west of the start (she is facing north at the end, which does not matter).
Answer: (b) west
Example 4
Ravi walks 5 km east, then turns left and walks 2 km, then turns right and walks 4 km, then turns right and walks 2 km. How far is he from his starting point?
(a) 11 km (b) 9 km (c) 10 km (d) 12 km
- Track east–west and north–south separately (east and north positive).
- Net: 9 km east and 0 km .
- Distance = √(9² + 0²) = √81 = 9 km.
Answer: (b) 9 km
Example 5
Meena walks 2 km south, then turns left and walks 3 km, then turns left and walks 2 km, then turns left and walks 3 km, then turns right and walks 6 km. In which direction is she now from her starting point?
(a) north (b) north-west (c) south (d) south-east
- Net displacement: 0 km (none east–west), 6 km north.
- So she is to the north of the start (she is facing north at the end, which does not matter).
Answer: (a) north
Example 6
Ravi walks 10 km north, then turns left and walks 8 km, then turns left and walks 12 km, then turns right and walks 3 km, then turns right and walks 2 km. How far is he from his starting point?
(a) 13 km (b) 14 km (c) 11 km (d) 12 km
- Track east–west and north–south separately (east and north positive).
- Net: 11 km west and 0 km .
- Distance = √(11² + 0²) = √121 = 11 km.
Answer: (c) 11 km
Example 7
Ravi walks 3 km west, then turns right and walks 12 km, then turns left and walks 6 km. How far is he from his starting point?
(a) 16 km (b) 12 km (c) 21 km (d) 15 km
- Track east–west and north–south separately (east and north positive).
- Net: 9 km west and 12 km north.
- Distance = √(9² + 12²) = √225 = 15 km.
Answer: (d) 15 km
Example 8
Meena walks 8 km west, then turns right and walks 5 km, then turns right and walks 4 km, then turns right and walks 8 km. In which direction is she now from her starting point?
(a) south (b) south-east (c) north-east (d) south-west
- Net displacement: 4 km west, 3 km south.
- So she is to the south-west of the start (she is facing south at the end, which does not matter).
Answer: (d) south-west
- Ignore the final facing direction unless the question asks for it.
- Look for Pythagorean triples: 6 and 8 → 10.
- Cancel opposite legs first (5 km north then 5 km south = 0).
- Turning relative to the page instead of the walker's facing direction.
- Answering the direction of the start from the end (the reverse).
- Adding distances along the path instead of measuring the straight line.
Practice set
Attempt all 12 questions (about 90 seconds each), then check the worked solutions below.
Q1. Meena walks 2 km north, then turns right and walks 3 km, then turns left and walks 2 km. In which direction is she now from her starting point?
(a) north (b) north-east (c) south-west (d) north-west
Q2. Meena walks 3 km west, then turns left and walks 6 km, then turns left and walks 3 km, then turns left and walks 5 km. In which direction is she now from her starting point?
(a) south (b) west (c) north-east (d) north
Q3. Meena walks 10 km north, then turns right and walks 8 km, then turns right and walks 2 km, then turns right and walks 8 km, then turns left and walks 15 km. In which direction is she now from her starting point?
(a) north (b) south-east (c) south (d) north-east
Q4. Ravi walks 8 km south, then turns left and walks 4 km, then turns left and walks 8 km, then turns left and walks 15 km. How far is he from his starting point?
(a) 11 km (b) 12 km (c) 14 km (d) 13 km
Q5. Meena walks 4 km south, then turns right and walks 8 km, then turns left and walks 2 km. In which direction is she now from her starting point?
(a) north (b) south-east (c) north-east (d) south-west
Q6. Meena walks 6 km west, then turns left and walks 8 km, then turns left and walks 12 km, then turns left and walks 10 km, then turns left and walks 6 km. In which direction is she now from her starting point?
(a) north-west (b) south-west (c) south (d) north
Q7. Ravi walks 15 km north, then turns left and walks 12 km, then turns left and walks 6 km. How far is he from his starting point?
(a) 12 km (b) 15 km (c) 16 km (d) 21 km
Q8. Ravi walks 12 km west, then turns right and walks 15 km, then turns right and walks 10 km, then turns left and walks 4 km, then turns right and walks 2 km. How far is he from his starting point?
(a) 22 km (b) 21 km (c) 19 km (d) 20 km
Q9. Ravi walks 4 km north, then turns left and walks 15 km, then turns left and walks 2 km, then turns right and walks 6 km, then turns left and walks 2 km. How far is he from his starting point?
(a) 23 km (b) 21 km (c) 22 km (d) 24 km
Q10. Meena walks 15 km north, then turns right and walks 6 km, then turns left and walks 6 km, then turns right and walks 2 km, then turns right and walks 6 km. In which direction is she now from her starting point?
(a) north (b) north-west (c) south-west (d) north-east
Q11. Ravi walks 2 km south, then turns left and walks 15 km, then turns right and walks 6 km. How far is he from his starting point?
(a) 17 km (b) 15 km (c) 23 km (d) 18 km
Q12. Meena walks 5 km east, then turns left and walks 15 km, then turns left and walks 5 km, then turns left and walks 10 km. In which direction is she now from her starting point?
(a) south (b) west (c) north (d) south-west
Q1 – (b) north-east. Net displacement: 3 km east, 4 km north. So she is to the north-east of the start (she is facing north at the end, which does not matter).
Q2 – (a) south. Net displacement: 0 km (none east–west), 1 km south. So she is to the south of the start (she is facing north at the end, which does not matter).
Q3 – (c) south. Net displacement: 0 km (none east–west), 7 km south. So she is to the south of the start (she is facing south at the end, which does not matter).
Q4 – (a) 11 km. Track east–west and north–south separately (east and north positive). Net: 11 km west and 0 km . Distance = √(11² + 0²) = √121 = 11 km.
Q5 – (d) south-west. Net displacement: 8 km west, 6 km south. So she is to the south-west of the start (she is facing south at the end, which does not matter).
Q6 – (d) north. Net displacement: 0 km (none east–west), 2 km north. So she is to the north of the start (she is facing west at the end, which does not matter).
Q7 – (b) 15 km. Track east–west and north–south separately (east and north positive). Net: 12 km west and 9 km north. Distance = √(12² + 9²) = √225 = 15 km.
Q8 – (c) 19 km. Track east–west and north–south separately (east and north positive). Net: 0 km and 19 km north. Distance = √(0² + 19²) = √361 = 19 km.
Q9 – (b) 21 km. Track east–west and north–south separately (east and north positive). Net: 21 km west and 0 km . Distance = √(21² + 0²) = √441 = 21 km.
Q10 – (d) north-east. Net displacement: 8 km east, 15 km north. So she is to the north-east of the start (she is facing south at the end, which does not matter).
Q11 – (a) 17 km. Track east–west and north–south separately (east and north positive). Net: 15 km east and 8 km south. Distance = √(15² + 8²) = √289 = 17 km.
Q12 – (c) north. Net displacement: 0 km (none east–west), 5 km north. So she is to the north of the start (she is facing south at the end, which does not matter).
- Sketch on x–y axes
- √(x² + y²)
- Turns are relative to facing
- Morning shadow west
