Patwari Exam · Reasoning
Direction & Distance in Reasoning
This note explains the 8 directions, turning rules, and the Pythagoras theorem used in direction-and-distance questions.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- 8 directions
- 8 directions: North (N), South (S), East (E), West (W), NE, NW, SE, SW.
- Sunrise-sunset rule
- Sunrise in the east, sunset in the west — the shadow falls in the opposite direction.
- Turning right
- Turning right: North → East → South → West (clockwise).
- Turning left
- Turning left: North → West → South → East (counter-clockwise).
- Worked example
- Example: A walks 5 km north, then turns right and walks 3 km → he is now to the north-east; straight-line distance from the starting point = √(5²+3²) = √34 km.
- Pythagoras theorem
- Pythagoras theorem: straight-line distance = √(perpendicular² + base²) — when a right angle is formed.
- Exam tip
- Exam tip: always draw a diagram on paper; note both direction and distance.
Frequently Asked Questions
How many directions are there in direction-and-distance questions?+
There are 8 directions — North (N), South (S), East (E), West (W), NE, NW, SE, SW.
How does the order of directions change on turning right?+
On turning right, the direction changes clockwise, e.g. North → East → South → West.
Which formula is used to find the straight-line distance?+
When a right angle is formed, the Pythagoras theorem gives the straight-line distance = √(perpendicular² + base²) — e.g. after going 5 km north and 3 km right, the distance is √(5²+3²) = √34 km.