Direction & Distance Guide & Practice
Practice displacement, shadow-based direction, multi-step journeys, and two-person movement problems with shortcuts and free mock tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.
Practice Question Papers
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1. Fundamentals & Definitions
- Direction: The position of one thing with respect to another or a reference point.
- Distance: The measurement of the shortest distance (displacement) between two points.
- Starting Point (Origin): The point where the movement begins.
- Destination: The point where the movement ends.
- Main Directions: There are four main directions: North, South, East, and West.
- Sub-Directions: There are four sub-directions (also called cardinal directions): North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W).
- Turns:
- Right Turn: Always a clockwise (CW) turn.
- Left Turn: Always an anticlockwise (ACW) turn.
| Direction | Opposite Direction |
|---|---|
| North | South |
| East | West |
2. Core Concepts & Formulas
Types of Direction Problems
- Turns and Rotations: A person or object makes a series of left/right turns (or clockwise/anticlockwise rotations by a specific degree). The final direction or position is asked.
- Distance and Displacement: Displacement is the shortest distance between the initial and final points. This is different from the total distance traveled. If a person returns to the starting point, their displacement is zero.
- Shadow-Based Problems: These questions rely on the position of the sun.
- From sunrise until just before noon (12 PM), a shadow is cast to the West.
- From just after noon (12 PM) until sunset, a shadow is cast to the East.
- At exactly 12 PM (noon), there is no shadow.
- A shadow is always cast on the opposite side of the sun.
- Coded Directions: Directions and distances are represented by symbols. You must decode the symbols to solve the puzzle.
Finding the Shortest Distance
To find the shortest distance (displacement) between the starting and ending points, the Pythagorean theorem is used. This applies when the movement forms a right-angled triangle.
Formula: Hypotenuse² = Base² + Perpendicular²
(or H² = B² + P²)
Where:
- H (Hypotenuse): The shortest distance between the start and end points.
- B (Base): The horizontal distance covered.
- P (Perpendicular): The vertical distance covered.
Typical Exam Weightage
| Exam | Typical Questions |
|---|---|
| SSC (CGL / CHSL / MTS) | 1–2 questions |
| Banking (IBPS / SBI) | 1–2 questions |
| Railways (RRB) | 1 question |
A coordinate-grid sketch is the single most reliable technique — mental tracking of turns is where most errors happen.
Figures are typical ranges based on recent-year patterns, not a guarantee for any specific upcoming paper — always cross-check against the latest official syllabus and previous-year papers for Direction & Distance.
Solved Examples
Question: Renu is facing South. She turns 90 degrees left, then she turns 90 degrees right, then she turns 180 degrees left. Now in which direction is she facing?
View Detailed Solution & ExplanationHide Explanation
- Initial Direction: Renu is facing South.
- Turns 90° left: Facing South, a 90° left turn makes her face East.
- Turns 90° right: From East, a 90° right turn makes her face South again.
- Turns 180° left: From South, a 180° left turn makes her face North. (A 180° turn is a complete reversal, regardless of left or right).
- Final Direction: Renu is now facing North.
Question: A nurse moved 90 m in the East in a hospital to look for her duty doctor, then she turned right and went 20m. After this, she turned right and after going 30 m she reached the I.C.U but the Doctor was not there. From there she went 100 m to her north and met her doctor. What is the shortest distance between her starting point and the doctor's location?
View Detailed Solution & ExplanationHide Explanation
- Let the starting point be A. The nurse moves 90m East to point B. (A -> B = 90m)
- She turns right (South) and moves 20m to point C. (B -> C = 20m)
- She turns right (West) and moves 30m to point D. (C -> D = 30m)
- From D, she moves 100m North to point E, where she meets the doctor.
- To find the shortest distance (AE), we use Pythagoras' theorem.
- Calculate the net horizontal distance (Base): The nurse moved 90m East and then 30m West. So, the net distance from the starting vertical line is
90m - 30m = 60m. - Calculate the net vertical distance (Perpendicular): The nurse moved 20m South and then 100m North. So, the net distance from the starting horizontal line is
100m - 20m = 80m. - Apply the formula
H² = B² + P²:AE² = 60² + 80²AE² = 3600 + 6400AE² = 10000AE = √10000 = 100m - The shortest distance is 100m.
Question: On an evening at 4 PM, Seeta and Reema are sitting in a garden facing each other. If Reema's shadow falls behind her, which direction is Seeta facing?
View Detailed Solution & ExplanationHide Explanation
- Time of Day: It is evening. In the evening, the sun is in the West.
- Shadow Direction: Since the sun is in the West, all shadows are cast towards the East.
- Reema's Position: Reema's shadow falls behind her. This means her back is towards the direction of the shadow (East). If her back is to the East, she must be facing West.
- Seeta's Position: Seeta and Reema are facing each other. Since Reema is facing West, Seeta must be facing the opposite direction.
- Final Direction: Seeta is facing East.