*Monday, June 25th, 2018*

The direction questions are one of the most repeated questions in the CAT Exam. Apart from CAT, direction and distance reasoning questions are also frequently asked in most of the MBA exams and other competitive exams. The test-takers are suggested to attempt these questions effectively as they are scoring and easily-solvable.

The direction and distance reasoning questions, as the name implies, includes two types of questions i.e.:

**Direction Sense Test****Distance Related questions**

The questions based on directions require the candidates to identifying the direction of an individual or shadow from a set of statements. We should know of some of the important points which helps to solve the questions with ease.

In general, there are four main directions i.e. North, South, East and West. Apart from these four, there are four additional directions derived from the main ones. They are called North-East, North-West, South-East and South-West. A chart is given below for reference.

A lot of times questions in CAT are asked regarding casting of shadows. It is important and useful to know the below concepts to understand

- If a man faces a rising sun, his shadow will always be in the west.
- If a man faces north, his shadow will be on his right during sunrise and on his left during sunset.
- Similarly, if a man faces south, his shadow will be on his left during sunrise and on his right during sunset.
- In mid-noon, no shadows are seen as the sun’s rays are vertically downwards.

In most of the direction and distance questions, it is required to calculate a certain parameter from the question statement. The questions can be related to the total distance walked, shortest path, the distance between two entities, etc.

While solving the distance related question, one must be thorough with the ** Pythagorean Theorem **to be able to solve most of the questions. The Pythagorean Theorem is used to calculate the shortest path traveled, the minimum distance between two points, etc. A couple of examples and cat questions are given below to illustrate the direction and distance questions better.

- A person facing north, on taking left will face towards west and on taking the right turn towards east.
- A person facing west, on taking left will face towards south and on taking right turn towards north.
- A person facing east, on taking left will face towards north and on taking the right turn towards south.
- A person facing south, on taking left will face towards east and on taking the right turn towards west.

** Example 1:** Airplanes A, B, C and D started flight towards east. After flying 125 kms planes A and D flew towards right while planes B and C flew towards left. After 115 km, planes B and C flew towards their left while planes A and D also turned towards their left. In which directions are the airplanes A, B, D, C respectively flying now?

- North, South, East, West
- East, West, West, East
- East, West, East, West
- South, North, North, South

**Solution:**

- Let us look at A and D first. After flying for 125 kms, A and D would still be in east direction. Now , they take a right turn which makes their direction as south. From south, if you take a left, you will again come in the east direction. So planes A and D are in east direction.
- Now, let us look at planes B and C. After flying for 125 kms, B and C would still be in east direction.

From east direction, they take a left turn which means now they are in north. From north, they again take a left which makes them land in the west.

So correct answer would be: East, west, East, West (Option C)

**Example 2: **Aman starts from his house and walks 2 km east up to his class and turns southwards and walks 1 km up to his friend’s house. At the friend’s house, he turns to east and walks 2 km up to his school. He then turns northwards and walks 4 km to the garden. How far is he from his house?

a. 5 km

b. 7 km

c. 4 km

d. 2.5 km

__Solution:__

**Distance from his house = **

= 5 km

**Solution:** He is 5 Km from his house.

** Example 3: **One evening Amit and Gaurav were talking to each other face to face at a crossing. If Gaurav’s shadow was exactly to the left of Amit, which direction was Amit facing?

** Solution**: Since Gaurav and Amit are standing face to face, if Gaurav’s shadow is to the left of Amit, it would be to the right of Gaurav.

Now remember point about shadows above:

- If a man faces north, his shadow will be on his right during sunrise and on his left during sunset.
- Similarly, if a man faces south, his shadow will be on his left during sunrise and on his right during sunset.

We know from the question that it is sunset and shadow is to the right of Gaurav.

Using point 2 above, Gaurav is facing south. Hence, Amit is facing north.

**Solution:** Gaurav is facing north.

** Example 4: ** Y is in the east of X which is in the north Z. If P is in the south of Z, then in which direction of Y, is P?

** Solution: **It is best to solve these type of questions by drawing diagrams. Let us first draw z, and then from there we can draw other points as well.

Looking at the above picture, it becomes very clear that P is in the south west of Y.

** Example 5: **Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to the north. In which direction the minute hand will point at 09:15 P.M. ?

** Solution: ** This question becomes very easy once we draw a clock at align the hour hand at 6 P.M. with the north direction. Now, in the same clock aligned as before, we move the minute and hour hands in such a way that now it is 09:15 P.M.

As we can see from the image above, minute hand at 09:15 P.M points to the west.

** Example 6**: A child is looking for his father. He went 90 meters in the East before turning to his right. He went 20 meters before turning to his right again to look for his father at his uncle’s place 30 meters from this point. His father was not there. From here he went 100 meters to the North before meeting his father in a street. What is the smallest distance between the starting point and his father’s position?

__Solution: __

For this type of question, Keep in mind that when a person moves to his left side, he will move towards anti- clockwise direction and when a person moves to his right side, he will move towards clockwise direction. When a question says moved towards left or right side, we assume that the movement is at an angle of 90 degrees.

The movement of the child from A to E is as shown in fig.

Clearly, the child meets his father at E.

Now, AF = (AB – FB)

= (AB – DC) = (90 – 30) m = 60 m.

EF = (DE – DF) = (DE – BC)

= (100 – 20) m = 80 m.

Now the distance is square root of (602 + 802), which will be 100 meters.

** Example 7**: Kabul is located 2 km away to the north-west Punjab. Rohtak is located 2 km in the south-west direction from Kabul. Melghat is another place and is located 2 km away in the north-west of Rohtak. Talu is located 2 km away in the south-west direction from Melghat. In which direction is Talu from Punjab?

** Solution**: Let us denote these letters by their initials.

Distances are same i.e. 2km so P, R and T fall in a single line. While K and M are in a single line. Hence, we can see that Talu is to the West of Punjab.

__Example 8__**: **** **Arya and Bindya start from a point simultaneously. Arya moves to his East and travels 12 km, and Bindya moves to her south and travels 12 km. Arya takes a 270° anti-clock wise turn and travels 12 km. Bindya takes a 90° clock wise turn and runs 18km. Then Bindya goes 30km in same line in exactly opposite direction. Which of the following is true regarding their positions?

1) Bindya has travelled 30 km more than Arya

2) both are to the south east of original position

3) both are at the same point

__Solution: __

__I__n the above figure, we denote Arya’s movement by red line and Bindya’s movement by blue line. We see that the final destination for both Bindya and Aryan is same and that both are to the south east of original position. Hence, 2 and 3 are correct.

** Conclusion:** We can clearly see from the above example that knowledge of basic concepts can go a long way in reducing the time you take to solve problems, along with improving your accuracy. Make sure you place sufficient emphasis on the topics such as ‘direction based questions’, and your performance is surely meant to improve.

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Pls correct these :

If a man faces north, his shadow will be on his right during sunrise and on his left during sunset.

Similarly, if a man faces north, his shadow will be on his right during sunrise and on his left during sunset.