Basic Concept Of DIRECTION And DISTANCE

It is introduced in reasoning tests to gauge the ‘sense of direction’ of the candidate. But as the reasoning tests have become frequent in competitive examinations, the usage of such questions has been increased. Today, direction tests are not only used in reasoning tests for checking ‘sense of direction’ but also for logical comprehension of particular situations.

Basic Directions

• There are four main directions:
  East, West, North and South.

• There are four cardinal directions:
  North-East (N-E), North-West (N-W), South-West (S-W) and South-East (S-E).

One should be aware of basic geometric concepts to find the shortest distance, such as the Pythagoras Theorem.

(Hypotenuse)² = (Base)² + (Perpendicular)²

AC² = BC² + AB²

AC = √(BC² + AB²)

Solved Example

Type-1

Question 1

Ramu moves 3 km towards the North and turns to the right up to 4 km. What is the distance from his starting point?

Options:

(a) 10 cm.                                                     
(b) 8 km
(c) 5 km
(d) 14 km

Solution

According to the Pythagoras Theorem:

AC² = AB² + BC²

AC² = 3² + 4²

AC² = 9 + 16

AC = √25 = 5 km

Therefore, the distance from his starting point = 5 km.

Correct Answer: (c) 5 km

Question 2

A man walks 6 km to the east and then turns to the south and walks 5 km. Again, he turns to the east and walks 6 km. Next, he turns northward and walks 10 km. How far is he now from his starting point?

(a) 15 km
(b) 13 km
(c) 7 km
(d) 12 km

Solution:

BO = CD = 6 km

BC = OD = 5 km

∴ EO = ED − OD = (10 − 5) km = 5 km

AO = AB + BO = 6 + 6 = 12 km

∴ AE² = AO² + OE²

AE² = 12² + 5²

AE² = 144 + 25

AE² = 169

AE = √169 = 13 km

Answer: (b) 13 km

Question 3

Rahul walks 2 km northward and takes a left turn and walks 5 km and then turns right, walks 3 km and again turns right, walks 5 km. In which direction is he now from the starting point?

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

Solution:

Rahul walks 2 km northward.

Then he turns left and walks 5 km westward.

Next, he turns right and walks 3 km northward.

Again, he turns right and walks 5 km eastward.

The 5 km westward and 5 km eastward distances cancel each other.

Total distance northward = 2 + 3 = 5 km.

Answer: North

Question 4

A person is facing North. He turns to his left and moves 100 m. Then he turns his right twice and goes straight 50 m and 25 m respectively. Then he turns to right up to 135° and starts moving. Now in which direction is he moving?

(a) South-East
(b) South-West
(c) South
(d) West

Solution:

Therefore, he is moving towards South-West.

Answer: (b) South-West

Question 5

Raju left for his office in his car. He drove 15 km towards North and then 10 km towards West. He then turned to the South and covered 5 km. Further, he turned to the East and moved 8 km. Finally, he turned right and drove 10 km. How far and in which direction is he from his starting point?

(a) 2 km West
(b) 2 km East
(c) 3 km North
(d) 6 km North

Solution:

Raju’s distance from the starting point A:

AF = (BC − DE) = (10 − 8) km = 2 km

∴ Answer is 2 km West.

Answer: (a) 2 km West

Direction and Distance – Practice Set for Banking/SSC/Railway

1. If A is to the south of B and C is to the east of B, in which direction is A with respect to C?

(a) North-east (b) North-west (c) South-east (d) South-west

2. A is 40 m South-west of B. C is 40 m South-east of B. Then, C is in which direction of A?

(a) East (b) West (c) North-east (d) South

3. Raj travelled from a point X straight towards east to Y at a distance of 80 metres. He turned right and walked 50 metres, then again turned right and walked 70 metres. Finally, he turned right and walked 50 metres. How far is he from the starting point?

(a) 10 metres (b) 20 metres (c) 50 metres (d) 70 metres

4. Aditya went 15 kms to the west from his house, then turned left and walked 20 kms. He then turned East and walked 25 kms and finally turning left covered 20 kms. How far was he from his house?

(a) 5 kms (b) 10 kms (c) 40 kms (d) 80 kms

5. From his house, Lokesh went 15 kms to the North. Then he turned West and covered 10 kms. Then, he turned South and covered 5 kms. Finally, turning to East, he covered 10 kms. In which direction is he from his house?

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

6. ‘Z’ started walking straight towards South. He walked a distance of 15 metres and then took a left turn and walked a distance of 30 metres. Then he took a right turn and walked a distance of 15 metres again. Z is facing which direction?

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

7. Alok walked 30 metres towards east and took a right turn and walked 40 metres. He again took a right turn and walked 50 metres. Towards which direction is he from his starting point?

(a) South (b) West (c) South-West (d) South-East

8. A man is facing north-west. He turns 90° in the clockwise direction and then 135° in the anticlockwise direction. Which direction is he facing now?

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

9. A man is facing north-west. He turns 90° in the clockwise direction, then 180° in the anticlockwise direction and then another 90° in the same direction. Which direction is he facing now?

(a) South (b) South-west (c) West (d) South-east

10. I am facing east. I turn 100° in the clockwise direction and then 145° in the anticlockwise direction. Which direction am I facing now?

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