Distance and Direction: Definition, Reasoning Questions, Examples

Types of Distance and Direction Reasoning Questions

1. Passage Based

2. Angle Based

3. Shadow Based

Let’s understand each type in detail -

1) Passage-Based Distance and Direction Reasoning Questions

In this type of question, information is given in passage form. In such passages, the movement of a particular person is given from the starting point to the ending point or vice versa.

Example:
Directions: Kartik walks 40 m straight from his home towards the North. Then, he turns left and walks 25 m. He turns left again and walks 15 m. Finally, he turns left and walks 25 m to reach Point X. What is the shortest distance between his home and Point X?

1) 22 m

2) 25 m

3) 15 m

4) 55 m

Solution:

Firstly, we will draw the diagram as per the given instructions –

Point A is the starting point and X is the endpoint, so the distance between them is XA.

XA = 40 – 15 = 25

So, the shortest distance between Kartik's home and point X is 25 m. Hence, the second option is correct.

Example:
Directions: Bismita walks 200 m towards the East and then turns right and walks 210 m to reach a hospital. What is the shortest distance between the starting point and the hospital?

1) 310 m

2) 290 m

3) 220 m

4) 260 m

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and B is the endpoint.

For the shortest distance (AB) between the starting point and the endpoint,

With the help of Pythagoras' formula:

$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2$,

⇒ $(AC)^2 + (BC)^2 = (AB)^2$

⇒ $(200)^2 + (210)^2 = (AB)^2$

⇒ $40000 + 44100 = (AB)^2$

⇒ $(AB)^2 = 84100$

⇒ $AB = 290$ m

So, the shortest distance between Bismita's starting point and the hospital is 290 m. Hence, the second option is correct.

2) Angle-Based Distance and Direction Reasoning Questions

In this type of question, the information is given in the angle form, like one has turned 90͒ / 45͒ and so on. Let’s understand this with an example -

Example:
Directions: A girl is standing facing towards the east. She turns 45 degrees in the anticlockwise direction and then turns 180 degrees in the clockwise direction. Which direction is she facing now?

1) West
2) South
3) North
4) South-West

Solution:

As per the given information, the direction the girl will look is as follows –

Therefore, the girl is facing towards the southwest direction. Hence, the fourth option is correct.

3) Shadow-Based Distance and Direction Reasoning Questions

In this type of question, the direction of the shadow of a person is asked. To solve this type of question, the understanding of the direction of the sun in the morning and the evening plays an important role. Shadows always fall on the opposite side of the Sun. The shadow falls in the west direction in the morning as the sun rises in the east. Similarly, in the evening, the shadows fall in the east direction, but at 12 PM no shadow will be formed.

Example:
Directions: At the time of sunrise, Diksha and Arpita are sitting in a park with their backs facing each other. If the shadow of Diksha falls to the right of Arpita, then in which direction is Arpita facing?

1) North

2) East

3) West

4) South

Solution:

Given: At the time of sunrise, Diksha and Arpita are sitting in a park with their backs facing each other.

At the time of Sunrise, the Sun is in the east direction, and the shadow will be in the west direction. So, it is given that the shadow is on the right side of Arpita. Therefore, Arpita will face towards the South direction.

Hence, the fourth option is correct.

Top Tips to Solve Distance and Direction-Based Questions

The aspirants must follow the tips given below to solve the distance and direction reasoning questions.

Tip 1: To solve the distance and direction questions, the aspirants must understand the directions. There are four main directions and four sub-directions. The main directions are North, South, East, and West, whereas the sub-directions are North-East, North-West, South-East, and South-West.

Tip 2: After that, the aspirants must know about the right turn and left turn, which is generally asked in the distance and direction reasoning section. The aspirants must check the right and left sides with the position of their hands. It is the easiest method to learn about the left or the right side, or they must remember that the direction of the right turn is always clockwise, whereas the direction of the left turn is always anticlockwise.

Tip 3: The aspirant must learn the Pythagorean theorem to find out the shortest distance between the starting point to the final point.

Tip 4: The aspirants should always apply NESW in a clockwise direction if the clockwise or anticlockwise direction is not mentioned in the question. The North is opposite to the South and the East is opposite to the West.

Question Weightage of Distance and Direction Reasoning Questions in Competitive Exams

The number of Direction and Distance questions varies from exam to exam:

Useful Books for Distance and Direction Reasoning

This section lists some of the best books to learn distance and direction reasoning concepts for competitive exams. These resources provide clear explanations, solved examples, and practice questions to improve direction sense and problem-solving skills.

Verbal Reasoning Topics

This section highlights all the key verbal reasoning topics you need to master for competitive exams, covering concepts, question types, and essential skills. It gives you a quick roadmap of what to study, helping you understand the structure of verbal reasoning and how to prepare effectively for exams like CAT, SSC, RRB, IBPS, and banking tests.The most important verbal reasoning topics you must read:

Solved Examples of Distance and Directions

According to the different types, the practice questions for direction and distance are as follows -

1. Passage-based distance and direction questions

1. Directions: A person starts from point Z and moves 7 km towards the South. He turns right and moves 5 km, turns right and moves 3 km, then turns right and moves 1 km. He takes a left turn and moves 4 km to reach point X. How much and in which direction does he need to move now to reach point Z?

1) 4 km South

2) 4 km East

3) 4 km West

4) 6 km East

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the direction and distance to reach the point Z.

From the above diagram, the Z point is in the east direction and at a distance of (5 – 1) = 4km from point X. Hence, the second option is correct.

2. Directions: A boy walks 15 m north, turns right, and walks 20 m. Again, he turns right and walks 15 m. Finally, he turns to his left and moves 20 m. What is the distance now from his original position?

1) 40 m
2) 46 m
3) 50 m
4) 45 m

Solution:

According to the instructions given, the diagram is as follows –

Here, O is the starting point and D is the finishing point, and OD is the total distance from the starting point.

OA = 15m; AB = 20m; BC = 15m; CD = 20m

And, OD = 20 + 20 = 40m

So, the distance now from his original position is 40m. Hence, the first option is correct.

3. Directions: Manoj starts from point A and drives X km towards the south and then turns left and drives Y km. He then takes a right turn and drives for 4 km to reach point D. If Manoj drove a total of 17 km between Points A and D, and both X and Y are perfect squares where X > Y, then what is the value of X?

1) 4 km

2) 11 km

3) 5 km

4) 9 km

Solution:

According to the instructions given, the diagram is as follows –

Now, we have to find the values of X and Y.

Here, A is the starting point and D is the finishing point.

AB = X km; BC = Y km; CD = 4 km

And, the total distance between Points A and D is 17 km.

⇒ AD = AB + BC + CD

⇒ 17 = X + Y + 4

⇒ 17 – 4 = X + Y

⇒ 13 = X + Y

It is given that both X and Y are perfect squares where X > Y, so X = 9 km and Y = 4 km.

So, the value of X is 9 km. Hence, the fourth option is correct.

4. Directions: Starting from point A, an animal walked 15 m towards the East. It took a left turn and walked 25 m. Then, it took a right turn and walked 10 m. Again it took a left turn and walked 15 m. Finally, it took a left turn and walked 25 m. How far and in which direction is the animal now from the starting point A?

1) 25 m, East

2) 40 m, South

3) 40 m, North

4) 25 m, West

Solution:

Firstly, we will draw the diagram as per the given instructions –

From the above diagram, the endpoint is in the north direction from the starting point and at a distance of 40 m. Hence, the fourth option is correct.

5. Directions: Starting from point X, a person walked 20 m towards the South to reach point Y. From there, he took a left turn and walked 25 m to reach point Z. He then took a left turn and walked for another 20 m to reach point P. What is the approximate shortest distance between the points X and Z and in which direction is the person's final position with respect to point X?

1) 50 m, South East

2) 36 m, South East

3) 32 m, East

4) 46 m, North West

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the approximate shortest distance between points X and Z and in which direction is the person's final position with respect to point X.

Here, X is the starting point, Z is the endpoint, and the shortest distance between points X and Z = d

Using Pythagoras' theorem, we have

⇒ $(d)^2 = (20)^2 + (25)^2$

⇒ $(d)^2 = 400 + 625$

⇒ $(d)2 = 1025$

⇒ $d = 32.01 ~ 32$

From the above diagram, the endpoint (P) is in the east direction from the starting point (X), and the shortest distance between points X and Z is 32m. Hence, the fourth option is correct.

2. Angle-based distance and direction questions

1. Directions: Joseph starts for his school from his house. He first goes 2 km towards the west and then turns 90° clockwise and goes further 2 km to reach his school. In which direction is his house from his school?

1) Southeast

2) South

3) Northwest

4) North

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the direction of the school with respect to the house.

Therefore, the house is in the southeast direction with respect to the school. Hence, the first option is correct.

2. Directions: P started walking from north to south. She turned right at a right angle and then again right at a right angle. In which direction was she ultimately walking?

1) North

2) East

3) South

4) West

Solution:

Firstly, we will draw the direction and distance diagram according to the instructions –

Now, we have to find the direction in which P is moving.

So, P was facing in the north direction. Hence, the first option is correct.

3. Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?

1) North-East

2) North-West

3)South-East

4)South-West

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and D is the endpoint.

So, the person is facing in the northwest direction. Hence, the second option is correct.

4. Directions: Vijay walks 10 metres westward, then turns left and walks 10 metres. He then again turns left and walks 10 metres. He takes a 45° turn rightwards and walks straight. In which direction is he walking now?

1) South

2) West

3) South-East

4) South-West

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and E is the endpoint.

So, Vijay is walking in the southwest direction. Hence, the fourth option is correct.

5. Directions: Karan, facing south, moved straight 2 km and from there turned to his right 90° and travelled 2 km. Then he took a 45° turn to his left and travelled 1 km. Where would he be now concerning the starting point?

1) South Region

2) South-East Region

3) North-West Region

4) South-West Region

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now we have to find the direction of Karan concerning the starting point.

So, Karan is in the South-West region concerning the starting point. Hence, the fourth option is correct.

3. Shadow-Based Distance and Direction Questions

1. Directions: John, in the morning, started walking towards the north and then turned towards the opposite side of the sun. He then turns left again and stops. Which direction is he facing now?

1) North

2) West

3) South

4) East

Solution:

Firstly, we will draw the diagram as per the given instructions –

After walking towards the north direction, John turns toward the left direction (As the sun rises in the east direction and the opposite side of the east is west direction.)

So, John is facing towards the south direction. Hence, the third option is correct.

2. Directions: One morning, Raju walked towards the sun. After some time, he turned left and again to his left. Which direction is he facing?

1) North

2) South

3) East

4) West

Solution:

Given: One morning, Raju walked towards the sun, i.e., he walked towards the east direction. (Because in the morning, the Sun is in the east direction.)

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find which direction Raju is facing.

So, Raju is facing towards the west direction. Hence, the fourth option is correct.

3. Directions: Shama, during the time of sunset, started walking towards the opposite side of the sun and then she turned right and right again. What direction is she facing?

1) South

2) West

3) East

4) North

Solution:

Firstly, we will draw the direction and distance diagram according to the instructions given in the question

Shama started walking towards the opposite direction of the sun during sunset, i.e., she was walking in the East direction (because during sunset, the sun is in the west direction).

So, Shama is facing the west direction. Hence, the second option is correct.

4. Directions: One morning, Raju walked towards the sun. After some time, he turned left and again to his left. Which direction is he facing?

1) North

2) South

3) East

4) West

Solution:

Given: One morning, Raju walked towards the sun, i.e., he walked towards the east direction. (Because in the morning, the Sun is in the east direction.)

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find which direction Raju is facing.

So, Raju is facing towards the west direction. Hence, the fourth option is correct.

5. Directions: John, in the morning, started walking towards the north and then turned towards the opposite side of the sun. He then turns left again and stops. Which direction is he facing now?

1) North

2) West

3) South

4) East

Solution:

Firstly, we will draw the diagram as per the given instructions –

After walking towards the north direction, John turns toward the left direction (As the sun rises in the east direction and the opposite side of the east is the West direction.)

So, John is facing towards the south direction. Hence, the third option is correct.

Direction Sense Questions PDF Download

For more practice, you should attempt the online distance and direction mock test and download the e-book of distance and direction reasoning questions PDF below.

Download Now: Direction Sense Questions with Solutions PDF

Distance and Directions Questions for SRMJEE/ VITEEE

Distance and Direction questions in SRMJEE and VITEEE test your problem-solving and spatial reasoning skills, which are essential for engineering entrance exams. Regular practice of these questions improves speed, accuracy, and confidence during the test.

Q-1) Directions: Kritika walks 40 m towards the south. Then, turning to her right, she rides 30 m. Then, turning to her left, she rides 50 m. Again, she turns to her left and rides 30 m. How far (in m) is she from her initial position?

1) 65 m

2) 70 m

3) 80 m

4) 90 m

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the distance between the starting and end points –

Therefore, the distance between Kritika's final point and starting point = 40 + 50 = 90 m. Hence, the fourth option is correct.

Q-2) Directions: Kishore starts from a point and walks 6 km towards the east, and turning to his left, he moves 3 km. After this, he again turns to his left and moves 6 km. Now, how far is he from his starting point?

1) 3 km

2) 2 km

3) 4 km

4) 5 km

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the distance between the starting and endpoints.

In the figure, A is the starting point and D is the finishing point. So, AD is the distance from the starting point.

Here, AB = CD = 6 km

And, AD = BC = 3 km

So, the distance from the starting point is 3 km. Hence, the first option is correct.

Distance and Directions Questions for TANCET/ JIPMAT

Distance and Direction questions in TANCET and JIPMAT help assess your logical thinking and spatial reasoning skills. Practicing these problems enhances your ability to interpret movements, directions, and distances quickly, which is key to scoring well in these competitive exams.

Q-1) Directions: A migrating bird flies 40 km north, then turns east and flies 50 km, then turns north and flies 110 km, and then turns to its left and flies 50 km. Where is it now with reference to its starting position?

1) 150 km south

2) 150 km north

3) 70 km north

4) 70 km south

Solution:

As per the given information, the movement of the bird will look as follows –

The distance between the migrating bird's starting point and end point = 40 + 110 = 150 km

The distance between the migrating bird's starting and end points is 150 km, and the migrating bird is in the north direction with respect to its starting position. Hence, the second option is correct.

Q-2) Directions: A paperboy cycles 10 km east, then turns south and cycles 3 km, then turns west and cycles 6 km, then turns to his right and cycles 3 km. Where is he now with reference to his starting position?

1) 4 km west

2) 14 km east

3) 4 km east

4) 14 km west

Solution:

Firstly, we will draw the diagram as per the given instructions –

Now, we have to find the distance and the final position with respect to the starting position –

The distance between starting position and end point = 10 – 6 = 4 km

Therefore, the paperboy is in the East direction with respect to his starting position and the distance between his starting point and final point is 4 km. Hence, the third option is correct.

Distance and Directions Questions for CUET/ Bank Pre/ Insurance Pre exams

Distance and Direction questions are a crucial part of logical reasoning sections in exams like CUET, Bank Prelims, and Insurance Prelims. These problems test your ability to track movement, calculate distances, and determine directions accurately under time pressure. Mastering them can significantly boost your score in competitive exams.

Q-1) Directions: A man starts from a point, walks 5 km towards the east, turns right and walks 3 km, turns right again and walks. What is the direction he is facing?
1) North

2) South

3) West

4) South-West

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and D is the endpoint.

So, the man is facing in west direction. Hence, the third option is correct.

Q-2) Directions: If the South-East is changed to North and North-East to West and so on, then what will come in place of South?

1) South-West

2) North-East

3) South-East

4) North-West

Solution:

From the given information, South-East means North, and North-East means West.

We can see that, to determine the directions need to move 3rd steps in a clockwise direction.

So, South means northeast direction. Hence, the second option is correct.

Distance and Directions Questions for SSC/ RRB exams

Distance and Direction questions in SSC and RRB exams test your ability to track movements, calculate distances, and determine directions accurately. Practicing these helps improve speed and precision, which is crucial for scoring well in these competitive tests.

Q-1) Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?

1) North-East

2) North-West

3) South-East

4) South-West

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and D is the endpoint.

So, the person is facing in the northwest direction. Hence, the second option is correct.

Q-2) Directions: Rajneesh started walking towards the north. He took a left turn after walking 20 metres. He again took a right turn after walking 30 metres. Which direction is he facing now?

1) North

2) East

3) West

4) South

Solution:

Firstly, we will draw the diagram as per the given instructions –

Here, A is the starting point and D is the endpoint.

So, Rajneesh is facing in the north direction. Hence, the first option is correct.

Formulas and Tricks for Distance and Direction

Solving distance and direction reasoning questions quickly requires knowing the right formulas and applying them smartly. These formulas help you calculate exact distances, directions, and shortest paths without confusion.

Basic Distance Formula in Reasoning

The most important formula in direction and distance reasoning is the distance formula:

$\text{Distance} = \text{Speed} \times \text{Time}$

However, in reasoning problems, speed is often not given. Instead, you track movements in steps or units to find the total distance or the shortest distance between two points.

For shortest path problems where movements are at right angles:

$\text{Shortest Distance} = \sqrt{(\Delta x)^2 + (\Delta y)^2}$

Example:
If a person walks 3 km east and then 4 km north, the shortest distance from the starting point is:

$\sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = 5 \ \text{km}$

Shortcut Methods for Quick Calculation

When solving direction and distance questions with answers, you can save time with these tricks:

Tip: Always draw a small diagram while solving. It helps you visualize the turns and avoid mistakes in direction reasoning.

Pythagoras Theorem in Direction and Distance

In logical reasoning direction and distance questions, the Pythagoras theorem is your best friend for shortest path calculations when movements form a right-angled triangle.

The theorem states:

$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2$

Where:

• Hypotenuse = shortest distance between start and end points

• Base = horizontal movement (east-west)

• Height = vertical movement (north-south)

Example:
A person moves 5 km south, then 12 km east. The shortest distance:

$\sqrt{(5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \ \text{km}$

This method is especially useful for complex direction and distance reasoning questions with answers, where you need quick and accurate results without lengthy step-by-step distance addition.

Non-Verbal Reasoning Topics

Non-verbal reasoning focuses on problem-solving using visual information rather than words or numbers. It involves identifying patterns, relationships, and logical sequences in shapes, figures, and diagrams. Mastering topics like analogy, classification, figure series, cube and dice problems, mirror images, and paper folding can significantly improve accuracy and speed in competitive exams. For non-verbal reasoning must read the topics below:

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.