Questions on directional reasoning are a favorite with all examiners. You will find questions of this type in all almost all reasoning tests. Broadly speaking, the questions on this topic may be categorized into these types:
For purposes of convenience, always remember these four directions, irrespective of where a person starts from (i.e., whether house, office, park or any street),these directions will remain the same. And also, the starting point will always be the intersecting point of these two lines as shown in the figure alongside.Keeping this thing in mind, let us try to solve this poser.
EXAMPLE: A person starts from his office and goes 100 metre towards north. After turning to his right, he walks 50 metre. Thereafter, he again turns right and walks 100 metre. In which direction and at what distance is he from his office now?
In this case, we have to do as has been dictated by the examiner. First of all, he asks us to move 100 meter towards north. Thereafter, he asks us to move to our right, i.e. the east. Again, he requires us to move to our right, i.e.downwards towards the south. As illustrated in the figure alongside, a rectangle is formed consisting of two sides 100 meter and 50 meter. Obviously,the person is 50 meters way from his starting point and at the moment, he is in the eastern direction
EXAMPLE : Mallika starts from home and walks 80 metre towards the south. She turns to her left and walks 50 meters. She again turns to her right and walks 40 metre. She takes a turnt owards her left and walks 60 metre. She takes a final turn towards her left and walks 120 metre. Our problem now is to find her distance and direction from the starting point.
As usual, our starting point will be the point where the N-S and E-W lines intersect, as has been illustrated above. We follow her movement as has been asked of us in the question and finally arrive at a point in the east. Now the problem before us is to find her distance from the starting point. We will have to calculate it indirectly because there is no direct way to do so. If you look carefully, the two distances i.e. 50 and 60 metres joined together give us the distance travelled by her on the eastern side, taken from the starting point.If you transpose this line connecting 50 and 60 meters, you will see that this is exactly the distance traveled by her on the eastern side. So the answer in this case is 100 metres east.
EXAMPLE: Bhanu starts from her office in the morning at 9 a.m. to meet her friend Kanu. She walks 40 metre towards the west, then takes a right turn and walks 30 metres. What is her distance from thestarting point and in which direction is she now? Now this is posing a bit difficult question. As you can see for yourself, Bhanu is somewhere in the middle of the western and the northern direction. This is where the Pythagorean theorem comes into play. Look carefully, these two distances, 40 and 30 metres, are forming a right-angled triangle, if you supply the third side yourself as has been done alongside.
Just for repetition, the Pythagorean theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the perpendicular and the base.
Letus assume that the third (unknown) side is designated X. Applying the theorem,
X2= (30)2 + (40)2
X2= 900 + 1600 = 2500
Therefore, X = Ö2500 = 50 metre. As you can see, she is in the middle of the northern and the western sides. Therefore, combining these two sides, we say that she is at present in the north-west 50 metres away from her starting point.
EXAMPLE:
There is a town called Timbkatoo, the streets of which intersect each another at right angles. Chandu starts from his house in the morning at 9 a.m. and walks 10 metres towards the south. After taking aturn to his left, he travels 20 metres before turning to his right and moves another 30 metres. Thereafter, he travels 20 metre to his left and funnily takes a left turn and travels 50 metre. He reaches a point X. Simultaneously, Saraswati starts from the same point from which Chandu had started. She goes 20 metres tothe west before she turns to her left and walks 10 metre. Thereafter, she takes a right turn, walks 30 metres.Thinking that she has come in the wrong direction, finally, she turns to her right and walks 50 metre to reach point Y. You have to find out at what distance is Saraswati from Chandu?
To find out the distance between X and Y, we simply have to add up the horizontal distance as indicated by the arrows i.e. 10 m + 20 m + 20 m +20 m = 70 m, which is the correct answer.
Let’s imagine a case in which we are asked the distance between Y and the point from which Chandu had taken his last turn. To find this out, we should know the distance between X and Y (70 metre). The third side is the diastase between X and the point from which Chandu had taken his last turn (which is 50 m). From these two, we can calculate the hypotenuse of the right-angled triangle as indicated above by applying the Pythagorean theorem. Our answer comes out to be
One important precaution to be exercised in all such questions is that whenever a person takes a right or left turn, the movement must be presumed to be at 90 degrees to either of the N-S or E-W lines, unless specified otherwise. For example, if in a hypothetical case, a person first walks 15 meter towards the north side and then takes a right turn and walks 20 meter, the movement has to be assumed like this, not otherwise unless it has been specified.
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