Module 1 · IBPS PO Reasoning Ability

Direction & Distance

Cardinal directions, path plotting, displacement, shadow problems.

Cardinal Directions · Path Plotting · Displacement · Shadow Problems

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Learning Objectives

Understand the fundamental concepts of Direction & Distance
Apply key formulas and techniques to solve problems
Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Direction & Distance?

Direction and distance questions test your spatial awareness â€” you must track movements on a plane using cardinal directions (North, South, East, West) and calculate final position relative to the starting point. These questions are a regular feature in SSC CGL Tier 1 reasoning section.

Key Concepts

1. Cardinal Directions: There are four main directions (North, South, East, West) and four intermediate directions (North-East, North-West, South-East, South-West). The angle between two adjacent main directions is 90Â°, and between a main and an intermediate direction is 45Â°.

2. Path Plotting: Draw a rough sketch showing each movement as an arrow. Mark distances. The final displacement is the straight-line distance from start to end, calculated using the Pythagoras theorem: dÂ² = (total East-West)Â² + (total North-South)Â².

3. Shadow Problems: In the morning (sunrise), the sun is in the East, so shadows fall towards the West. In the evening (sunset), the sun is in the West, so shadows fall towards the East. At noon, the sun is directly overhead, so there is no shadow.

4. Direction Changes: A right turn = +90Â° clockwise. A left turn = +90Â° counter-clockwise (anti-clockwise).

Solved Examples

Example 1 (Basic Path)

Rohan walks 10 km North, turns right and walks 5 km, then turns right again and walks 10 km. How far and in which direction is he from his starting point?

a) 5 km East b) 5 km West c) 10 km North d) 10 km West

Solution: a) 5 km East. Start at O. Walk 10 km North to A. Turn right (East), walk 5 km to B. Turn right (South), walk 10 km to C. Net displacement: East = 5 km, North = 10-10 = 0. So C is 5 km East of O.

Example 2 (Displacement)

A man walks 20 m East, then turns left and walks 15 m, then turns right and walks 25 m, then turns right and walks 15 m. How far is he from his starting point?

a) 40 m b) 45 m c) 50 m d) 55 m

Solution: b) 45 m. East: 20 + 25 = 45 m (first East 20, then after various turns another East 25). North-South: 15 North - 15 South = 0. Net displacement = 45 m East.

Example 3 (Shadow Problem)

One morning, Ravi and Raju are standing facing each other. Ravi's shadow falls to his left. Which direction is Raju facing?

a) North b) South c) East d) West

Solution: a) North. In the morning, sun is in the East, so shadows fall towards the West. If Ravi's shadow is to his left, then his left side is West. So Ravi is facing South (because when facing South, left is East... wait. When facing North: left is West, right is East. When facing South: left is East, right is West. When facing East: left is North, right is South. When facing West: left is South, right is North. If Ravi's shadow (West) is to his left, then left = West, so Ravi is facing South. Since Ravi and Raju are facing each other, Raju is facing North.

Shortcut Techniques

Draw a rough diagram for every question â€” it only takes 10 seconds and prevents mistakes.
Use a sign convention: East = +x, West = -x, North = +y, South = -y (or vice versa). Sum all x and y components to find net displacement.
For shadow problems, remember the sun's position: morning â†’ East, evening â†’ West.
A person's left side depends on their facing direction, not yours!

Pro Tip

When a question says 'turns left' or 'turns right', it means the person turns from their current facing direction. Always update the facing direction after each turn. For example, if facing North and turning right, you face East.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Cardinal directions and path plotting — example movement with net displacement

Practice Questions

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