Direction and Distance – Complete Notes
Direction and Distance – Complete Notes
1. Introduction
The Direction and Distance chapter is a fundamental
topic in logical reasoning sections of competitive exams like CUET, CLAT, and
IPMAT. It evaluates a candidate’s ability to understand directions (North,
South, East, West) and determine distances and final positions using spatial
reasoning.
2. Basic Concepts
2.1 The Four Main Directions
- North
(N)
- South
(S)
- East
(E)
- West
(W)
These directions are opposite to each other:
- North
↔ South
- East ↔
West
2.2 The Four Intercardinal Directions
These are combinations of the main directions:
- North-East
(NE)
- North-West
(NW)
- South-East
(SE)
- South-West
(SW)
These are at 45° angles between the main directions.
3. Types of Questions
Type 1: Final Direction Determination
Determine the direction in which a person is facing after
taking a series of turns.
Example 1:
Q: A person starts facing North, then turns right, then
left, and finally right again. In which direction is he facing now?
Solution:
- Starts
facing North
- Right
turn → East
- Left
turn → North
- Right
turn → East
Answer: East
Type 2: Final Distance from Starting Point
Calculate the shortest distance from the initial position
after a series of moves.
Example 2:
Q: Rahul walks 5 km North, then 3 km East. What is the
shortest distance from the starting point?
Solution:
- Movement
forms a right-angled triangle
- Use
Pythagoras theorem:
Distance=Sqr root(52+32)= sqr root(25+9)= sqr root 34≈5.83 km
Answer: Approximately 5.83 km
Type 3: Position-Based Questions
Determine the direction of one object/person from another.
Example 3:
Q: A is standing 6 km North of B. C is 8 km East of B. What
is the direction of A with respect to C?
Solution:
Draw the positions:
- A is
6 km North of B
- C is
8 km East of B
So, A is North-West of C.
Answer: North-West
4. Turn Conventions
When a person is facing:
- North:
Right → East, Left → West
- East:
Right → South, Left → North
- South:
Right → West, Left → East
- West:
Right → North, Left → South
These are crucial in tracking movement directions
accurately.
5. Angle of Turns
Right-angle Turn (90°):
Common in questions when a person takes a simple left or
right.
180° Turn:
Used when a person turns back.
Example 4:
Q: A person facing East turns 180°. Which direction is he
facing?
Answer: West
6. Common Trap Areas
- Misinterpretation
of directions – Always visualize or draw.
- Right
vs. Left confusion – Note the current direction the person is facing.
- Inaccurate
distance calculations – Use Pythagorean theorem carefully.
- Reversing
directions – Turning back reverses direction completely.
7. Practice Questions with Solutions
Question 1:
Aman walks 10 m North, then turns right and walks 5 m.
Again, he turns right and walks 10 m. What is his final direction and how far
is he from the starting point?
Solution:
- 10 m
North
- Right
→ East, 5 m
- Right
→ South, 10 m
Final direction: South
From starting point: 5 m East (since vertical movement cancels)
Answer: South, 5 m away
Question 2:
Priya walks 6 m South, then turns left and walks 8 m. She
again turns left and walks 6 m. How far is she from the starting point?
Solution:
- 6 m
South
- Left
from South → East → 8 m
- Left
from East → North → 6 m
Final position is 8 m East of starting point.
Answer: 8 m
Question 3:
Ravi walks 7 km East, then turns North and walks 3 km. He
turns West and walks 4 km. Then he turns South and walks 3 km. How far is he
from the starting point?
Solution:
Track his path:
- East
→ 7 km
- North
→ 3 km
- West
→ 4 km (Net East: 3 km)
- South
→ 3 km (Net vertical: 0)
Net displacement = 3 km East
Answer: 3 km
8. Strategic Tips for Exams
- Always
draw rough diagrams. It avoids confusion and aids quick understanding.
- Memorize
direction logic. Keep a cheat sheet for practice:
- Facing
North: R → East, L → West
- Facing
East: R → South, L → North
- Practice
Pythagoras. Many questions rely on right triangles.
- Time
Management: Don’t spend too long on visualization—practice improves
speed.
9. Real-Exam Style Questions
CLAT Level:
Q: A person walks 5 km towards the North, then turns right
and walks 3 km. He then turns left and walks 5 km. In which direction is he
from the starting point?
Solution:
- North
→ 5 km
- Right
→ East → 3 km
- Left
→ North → 5 km
Net position: 10 km North, 3 km East
Answer: North-East
10.CUET/IPMAT Level:
Q: Rohan walked 15 m towards North, turned right and walked
10 m, turned right again and walked 5 m. He then turned left and walked 10 m.
How far is he from the starting point?
Solution:
- 15 m
North
- 10 m
East
- 5 m
South → Net vertical = 10 m North
- 10 m
East → Net horizontal = 20 m
Answer: Approx. 22.36 m
11. Quick Reference Table
|
Facing |
Right Turn |
Left Turn |
|
North |
East |
West |
|
East |
South |
North |
|
South |
West |
East |
|
West |
North |
South |
1. CUET 2023
Q1. Ravi walks 20 m North, then turns right and walks
30 m, then again turns right and walks 20 m. How far is he from the starting
point?
Answer: 30 m
Explanation: He returns parallel to the starting point, just 30 m to the
East.
2. CLAT 2022
Q2. A girl walks 100 m straight from her home to the
East, then turns left and walks 50 m, again turns left and walks 100 m. How far
is she from her home?
Answer: 50 m
Explanation: She ends up 50 m South of her home.
3. IPMAT 2022 (IIM Indore)
Q3. A person walks 10 m North, then 5 m East, then 5
m South. How far and in what direction is he from his starting point?
Answer: 5√2 m North-East
Explanation: Net movement: 5 m North, 5 m East → diagonal path.
4. CUET 2022
Q4. A car travels 12 km North, then 5 km East, then
12 km South. What is the final distance from the starting point?
Answer: 5 km
Explanation: Vertical motion cancels; only 5 km East remains.
5. CLAT 2021
Q5. A boy is facing East. He turns 270° in the
anti-clockwise direction. Which direction is he facing now?
Answer: South
Explanation: 270° anticlockwise from East → South
6. IPMAT 2021
Q6. Ritu walks 15 m West, then turns right and walks
10 m. Then she turns left and walks 5 m. What is the distance of her current
position from the starting point?
Answer: √(15² + 5²) = √250 ≈ 15.81 m
Explanation: Triangle formed with legs 15 m and 5 m.
7. CLAT 2020
Q7. Mohan walks 10 m towards the North. Then he turns
right and walks 10 m. Then he turns right again and walks 10 m. Then he turns
left and walks 10 m. How far is he from the starting point?
Answer: 20 m
Explanation: Final location is 20 m to the East.
8. IPMAT 2020
Q8. A man walks 3 km North, then 4 km East. What is
the shortest distance back to his starting point?
Answer: 5 km
Explanation: Classic 3-4-5 triangle.
9. CUET Mock Paper
Q9. A person walks 8 m North, then 6 m West, then 4 m
South. What is the distance and direction from the starting point?
Answer: √(6² + 4²) = √52 ≈ 7.21 m North-West
10. CLAT Mock Paper
Q10. Seema walks 20 m South, then turns right and
walks 30 m, then right again and walks 20 m. What is her final direction?
Answer: North
Explanation: Final leg is North (opposite of first leg).
11. CUET 2023
Q11. A person is facing West. He turns 90° clockwise,
then 180° counter-clockwise. What direction is he facing now?
Answer: South
Explanation: West → North → South
12. IPMAT 2023
Q12. A person walks 18 m towards East, turns left,
walks 12 m, and then turns right and walks 6 m. How far is he from the starting
point?
Answer: √(18² + 18²) = √648 = 18√2 ≈ 25.45 m
13. CLAT 2019
Q13. John is facing North. He turns 45° clockwise,
then another 45°. What direction is he facing?
Answer: East
Explanation: Total turn = 90° clockwise → East
14. IPMAT 2019
Q14. A student walks 5 m East, 3 m North, 5 m West,
and 3 m South. Where is he from the starting point?
Answer: Same position
Explanation: All movements cancel out.
15. CUET Sample
Q15. A dog runs 20 m North, then 10 m East, then 20 m
South. What is its distance from the starting point?
Answer: 10 m
Explanation: Net movement is 10 m East.
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