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RRB NTPC Direction & Distance

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This page covers RRB NTPC Direction & Distance with complete concept notes, 16 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Direction & Distance— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

You start from a point, follow given directions (North, South, East, West), and determine the final position or shortest distance back to start. The key is visualizing the path and using coordinate geometry or Pythagoras theorem

Key Rules

North is positive Y-axis, East is positive X-axis, South is negative Y-axis, West is negative X-axis. Always draw a rough diagram. Right turn means clockwise rotation (N→E→S→W). Left turn means anticlockwise rotation (N→W→S→E).

Formula BlockMemorise — at least one formula appears in every paper
Shortest Distance = √[(x2-x1)² + (y2-y1)²]
Displacement = Final position - Initial position
Right turn sequence: N→E→S→W→N (clockwise)
Left turn sequence: N→W→S→E→N (anticlockwise)
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC asks three main types - (1) Find final position after multiple movements (2) Calculate shortest distance between start and end points (3) Determine direction of final position from starting point. Questions often include multiple turns to confuse students.

ShortcutsUse these to save 30–60 seconds per question

Use coordinate method. Place starting point at origin (0,0). Move North = +Y, South = -Y, East = +X, West = -X.

Plot final coordinates and apply distance formula. This eliminates drawing errors.

Worked ExampleSolve this step-by-step before moving on

Ram starts from home, walks 4km North, then 3km East, then 2km South. Find shortest distance to reach home. Solution: Place home at (0,0). After 4km North: (0,4).

After 3km East: (3,4). After 2km South: (3,2). Final position = (3,2).

Shortest distance = √[(3-0)² + (2-0)²] = √[9+4] = √13 = 3.6km Worked Example 2: Sita walks 5km East, turns right, walks 12km, turns right again, walks 5km. How far is she from start? Solution: Start at (0,0). 5km East: (5,0). Turn right (now facing South), walk 12km: (5,-12).

Turn right again (now facing West), walk 5km: (0,-12). Distance from start = √[(0-0)² + (-12-0)²] = 12km Advanced Shortcut: For rectangular paths, if you return to same X or Y coordinate, the distance equals the remaining coordinate value. In example 2, X-coordinate returned to 0, so distance = Y-coordinate = 12km. Direction Shortcut: Final direction from start can be found using coordinates.

If final position is (a,b), then direction is determined by signs: (+,+) = Northeast, (+,-) = Southeast, (-,+) = Northwest, (-,-) = Southwest.

Exam TrapsCommon mistakes students make — avoid these

Students confuse left/right turns with compass directions. Remember that turns are relative to current facing direction, not absolute directions. If facing North and turn right, you face East.

If facing East and turn right, you face South. Always track current facing direction after each turn. Another major error is calculation mistakes in distance formula. Students forget to square the terms or make errors in square root calculation.

Practice mental calculation of common squares: 3²=9, 4²=16, 5²=25, 12²=144, 13²=169. Time-saving tip: Recognize special triangles. 3-4-5 triangle has hypotenuse 5. 5-12-13 triangle has hypotenuse 13. 8-15-17 triangle has hypotenuse 17. If coordinates match these patterns, you can instantly write the answer without calculation.

Key Points to Remember

  • Always place starting point at origin (0,0) for coordinate method
  • North = +Y axis, South = -Y axis, East = +X axis, West = -X axis
  • Distance formula: √[(x2-x1)² + (y2-y1)²]
  • Right turn sequence: N→E→S→W (clockwise rotation)
  • Left turn sequence: N→W→S→E (anticlockwise rotation)
  • Draw rough diagram to visualize the path before calculating
  • For rectangular paths returning to same coordinate, distance equals remaining coordinate
  • Track current facing direction after every turn to avoid confusion
  • Memorize special triangles: 3-4-5, 5-12-13, 8-15-17 for quick calculation
  • Final direction from start depends on coordinate signs: (+,+)=NE, (+,-)=SE, (-,+)=NW, (-,-)=SW

Exam-Specific Tips

  • Pythagoras theorem: c² = a² + b² where c is hypotenuse
  • 3-4-5 triangle: sides 3, 4 give hypotenuse 5
  • 5-12-13 triangle: sides 5, 12 give hypotenuse 13
  • 8-15-17 triangle: sides 8, 15 give hypotenuse 17
  • √2 = 1.414 (for 45-degree movements)
  • √3 = 1.732 (for 60-degree movements)
  • Right angle = 90 degrees rotation
  • Straight angle = 180 degrees rotation
Practice MCQs

Direction & Distance — Practice Questions

16graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

Rajesh starts from his home facing North. He walks 8 km straight, then turns right and walks 6 km. After that, he turns left and walks 4 km. In which direction is Rajesh now facing, and how far is he from his starting point?

Practice 2easy

Priya walks 5 km towards the East from point A. She then turns left and walks 3 km. Next, she turns right and walks 2 km. Finally, she turns left and walks 4 km. How far is Priya from point A in a straight line?

Practice 3easy

Amit starts at point P facing South. He walks 10 km, then turns right and walks 8 km. He turns right again and walks 6 km. Finally, he turns left and walks 5 km. What is Amit's final position relative to point P?

Practice 4easy

Neha starts from her office facing East. She walks 12 km, turns left and walks 9 km. She then turns right and walks 7 km. What is the straight-line distance between her office and her final position?

Practice 5easy

Vikram walks 6 km North from point X. He then turns right and walks 8 km. After that, he turns left and walks 5 km. Finally, he turns right and walks 3 km. How far is Vikram from point X?

Practice 6medium

Rajesh starts from point A facing North. He walks 8 km, then turns right and walks 6 km. After this, he turns left and walks 4 km. Finally, he turns right and walks 5 km to reach point B. In which direction is point B with respect to point A, and what is the straight-line distance between them?

Practice 7medium

Rajesh starts at point A facing North. He walks 12 km North, then turns right and walks 8 km. After this, he turns left and walks 5 km. Finally, he turns right and walks 6 km to reach point B. What is Rajesh's final direction, and how far is he from his starting point A?

Practice 8medium

Rajesh starts from point A facing North. He walks 8 km, then turns right and walks 6 km. After this, he turns left and walks 4 km. Finally, he turns right and walks 3 km to reach point B. In which direction is point B with respect to point A?

Practice 9medium

Priya starts at point P facing South. She walks 10 km, turns left and walks 5 km, then turns right and walks 7 km. What is the straight-line distance between her starting point P and her final position?

Practice 10medium

Amit starts from point X facing North-East. He walks 12 km in that direction, then turns 90° clockwise and walks 8 km. What is his final direction from point X?

Practice 11medium

Vikram starts from point Q facing North. He walks 15 km, turns right and walks 8 km, turns right again and walks 15 km, then turns left and walks 6 km. How far is he from point Q?

Practice 12hard

Rajesh starts from point A facing North. He walks 8 km, then turns 90° left and walks 6 km. Next, he turns 90° right and walks 12 km. Finally, he turns 90° left and walks 4 km to reach point B. What is Rajesh's final direction and his displacement from point A?

Practice 13hard

Priya starts at point P facing Northeast. She walks 10 km in that direction, then turns 45° clockwise and walks 8 km. Next, she turns 90° counterclockwise and walks 6 km. What is her final position relative to P and her final facing direction?

Practice 14hard

Amit starts at point X facing South. He walks 5 km, then turns 90° right and walks 7 km. Next, he turns 90° left and walks 9 km. Then he turns 90° right and walks 4 km. Finally, he turns 90° left and walks 3 km to reach point Y. In which direction is Y from X, and what is the straight-line distance?

Practice 15hard

Sneha starts at point A facing Northwest. She walks 12 km in that direction, then turns 135° clockwise and walks 8 km. Next, she turns 45° counterclockwise and walks 10 km. What is her final position relative to A?

Practice 16hard

Rajesh starts at point A facing North. He walks 8 km, then turns 90° right and walks 6 km. After this, he turns 90° left and walks 4 km. Finally, he turns 90° right and walks 10 km to reach point B. What is Rajesh's final direction and his displacement from point A?

60-Second Revision — Direction & Distance

  • Remember: Use coordinate method with start point at (0,0)
  • Formula: Distance = √[(x2-x1)² + (y2-y1)²]
  • Trap: Track facing direction after each turn, not absolute directions
  • Shortcut: Recognize 3-4-5, 5-12-13, 8-15-17 triangles for instant answers
  • Technique: Right turns go N→E→S→W, left turns go N→W→S→E
  • Quick check: For rectangular paths, final distance often equals one coordinate value
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