Direction Test

 

Learning Objectives

• Introduction
• Concept of Direction
• Concept of Turn
• Concept of Minimum Distance

 

Introduction

In this test, the question consists of a sort of direction puzzle. A successive follow-up of direction is formulated and the candidate is required to ascertain the final direction or the distance between two points. The test is meant to judge the student ability to trace, follow and sense the direction correctly.

 

 

Concept of Direction

In our day to day life we form our concept of direction after seeing the position of the Sun, In fact, it is a universal truth that Sun rises in the East and goes down in the West. Thus, when we stand facing sunrise then our front is called East while our back is called West. At this position our left hand is in the northward and the right hand is in the southward. Let us see the following direction map that will make your concept more clear.

Direction Map: 

Note: On paper North is always on the top while South is always at the bottom. ·

Example: 1

1. A watch reads 4.30 if the minute hand points east/ in what direction does the hour hand point?   

(a) North                                                (b) North-west

(c) South-east                                         (d) North-east

(e) None of these

Ans.     (d) Explanation: Clearly to show 4.30, the position of the minute and hour hands of the clock will be as below, if the minute hand points East, the hour hand will point towards the North-East direction. 

· Example 2

2. Sanjeev walks 10 metres towards the South. Turning to the left, he walks 20 metres and then moves to his right. After moving a distance of 20 metres, he turns to the right and walks 20 metres. Finally, he turns to the right and moves a distance of 10 metres. How far and in which direction is he from the starting point?

(a) 10 metres North                                 (b) 20 metres South

(c) 20 metres North                                 (d) 10 metres South

(e) None of these

Ans.     (b) 

Explanation: The movements of Sanjeev from A to F are as shown in figure.

Clearly, Sanjeev's distance from starting point A

= AF = (AB + BF)

= AB + (BE - EF) = AB + (CD - EF) =

[10 + (20 - 10)] m = (10 + 10) m = 20 m

Also, F lies to the South of A

So, Sanjeev is 20 metres to the south of his starting point. ·

Example 3

I am facing south. I turn right and walk 20m. Then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m. Then I turn right again and walk 60 m. In which direction am I from the starting point?

(a) North                                    (b) North-west (c) East                                                

(d) North-east                         (e) None of these

Ans.     (d) 

Explanation: The movements of the person are from A to F, as shown in figure.

Clearly, the final position is F which is to the North-east of starting point A.

Concept of Turn

Left turn            =       Anti clockwise turn

Right turn          =       Clockwise turn Let us understand it through pictorial presentations

(i)                               (ii)         

(iii)                                      (iv)                                                

Important Points Regarding Directions

· If our face is towards North, then after left turn our face will be towards West and after right turn it will be towards East.

· If our face is towards South, then after left turn our face will be towards East and after right turn it will be towards West.

· If our face is towards East, then after left turn our face will be towards North and after right turn it will be towards South.

· If our face is towards West, then after left turn our face will be towards South and after right turn it will be towards North.

· If our face is towards North-West, then after left turn our face will be towards South-West and after right turn it will be towards North-East.

· If our face is towards South-West, then after left turn our face will be towards South-East and after right turn it will be towards North-West.

· If our face is towards South-East, then after left turn our face will be towards North-East and after right turn it will be towards South-West.

· If our face is towards North East, then after left turn our face will be towards North West and after right turn it will be towards South East.

· Example:

1. After walking 6 km, turned right and covered a distance of 2 km, then turned left and covered a distance of 10 km. In the end, I was moving towards the north. From which direction did I start my journey?

         (a) North                                               (b) South

         (c) East                                                  (d) West

        (e) None of these

       Ans.     (b)

Explanation:

Clearly, the route is as shown in the adjoining diagram.

Thus, the started his journey from the South and moved northwards. 

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

(a) 20 metres                                          (b) 50 metres

(c) 70 metres                                          (d) 10 metres

(e) None of these

Ans.     (d)

Explanation: The movements of Raj are as shown in figure (X to Y Y to A A to B and B to C) Raj?s distance from the starting point \[=\text{ }XC\text{ }=\left( XY-YC \right)=\left( XY-BA \right)=\left( 80-70 \right)m=10m\] 

3. Facing the east, Rajesh turned left and walked 10 metres, then he turned to his left again and walked 10 m. He then turned 45° towards his right and went straight to 25 metres. In which direction from his starting point is he?

(a) South-west                                        (b) South-East

(c) North -west                                        (d) North-east

(e) East

Ans.     (c)

Explanation:

Clearly the route followed by Rajesh is as shown in figure. So matching his final direction with the direction diagram, he will be in North-west direction from the starting point. 

 

4. Five students A, B, C, D and E are sitting in a row. D is on the right of E. B is on the left of E             but is on the right of A. D is on the left of C, Who is sitting on the extremely left?

(a) A                                                    (b) B

(c) C                                                    (d) D

(e) None of these

Ans.     (a)

Explanation: D is the right of E means the order is ED. B is on the left of E but right of A means ABE. D is to the left C means DC. Combining the arrangements, we have ABEDC. So, A is to the extreme left.

Concept of Minimum Distance

Minimum distance between initial and last point 

\[{{h}^{2}}={{b}^{2}}+{{p}^{2}},\text{ }where\]

h = Hypotenuse

b = Base

p = Perpendicular

AB = BA is the minimum or shortest distance to reach A from B or to reach B from A.

Remember: This important rule is also known as 'Pythagoras Theorem".

· Example 1

A man walks 10 km towards north. From there he walks 6 km towards south. Then he walks 3 km towards east. How far and in which direction is he with reference to his starting point?

(a) 7 km east                                         (b) 5 km west

(c) 5 km north-east                           (d) 7 km west

(e) None of these

Ans.     (c)

Explanation: The movements of the man are as shown in the figure. (P to B, B to C, C to D) PC = (PB - BC) = (10 - 6) = 4 km. Clearly D is to North-east of P.

\[\therefore \] The man's distance from the starting point \[P{{D}^{2}}=P{{C}^{2}}+C{{D}^{2}}={{4}^{2}}+{{3}^{2}}=16+9=25.\] \[\Rightarrow PD=5\text{ }km.\] 

· Example 2

A person starts from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the destination is.

(a) 12km                                                (b) 15km

(c) 16km                                                (d) 18km

(e) None of these

Ans.     (b) 

Explanation: The movements of the person are as shown in figure.

Clearly, AB = 3 km

\[BC=3AB=\left( 3\times 3 \right)\text{ }km=9\text{ }km\]

\[CD=5AB=\left( 5\times 3 \right)km=15\text{ }km\]

Draw \[AE\bot CD\]

Then, CE = AB = 3 km and AE = BC = 9 km

DE = (CD - CE) = (15 - 3) km = 12 km

\[In\,\,\Delta AED,\,\,A{{D}^{2}}=A{{E}^{2}}+D{{E}^{2}}\]

\[\Rightarrow AD=\sqrt{{{9}^{2}}+{{(12)}^{2}}}\,\,km=\sqrt{225}\,\,km=15\,\,km\]

\[\therefore \]Required distance = AD = 15 km.

· Example 3

Lalit starts walking from a point P towards West. After some distance he takes right turn and walks to a point A. Now, his direction from P is definitely towards North-West and shortest or minimum distance to reach A is PA.

Explanation: Pictorial presentation explains the truth.

Let us see: 

N W = North West                               south

N E = North East

S W = South West

S E = South East

Commonly Asked Questions

1. A man walks 1 km towards East and then he turns to South and walks 5 km. Again he turns to East and walks 2 km, after this he turns to North and walks 9 km. Now, how far is he from his starting point?

(a) 3km                                                 (b) 4km

(c) 5km                                                              (d) 7km

(e) None of these

Ans.     (c)

Explanation: 

The movements of the man are as shown in figure (A to B, B to C, C to D D to E)

DF = BC = 5 km

EF = (DE - DF) = (9 - 5) km = 4km

BF = CD = 2 km

AF = AB + BF = AB + CD = (1 + 2) km = 3 km

\[\therefore \] Man's distance from starting point A

\[=\sqrt{A{{F}^{2}}+E{{F}^{2}}}=\sqrt{{{3}^{2}}+{{4}^{2}}}=\sqrt{25}=5km\]

 

2. Kamal walks from his house T towards East and after walking some distance he takes left turn and reaches his office O. If he has to return home driving exactly opposite to his office, which direction will he walk?

(a) North-West                                       (b) North-East

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

(e) None of these

Ans.     (c)

Explanation: Option (c) is correct.

Let us see: 

3. Rashmi's house is just opposite to Mansi's house. Rashmi goes towards North-East and reaches Mansi?s house. If Mansi has to go to Rashmi?s house, then in which direction should Mansi go?   

(a) South-West                                       (b) North-West

(c) South-East                                        (d) North-East

(e) None of these

Ans.     (a)

Explanation: Option (a) is correct because Rashmi's and Mansi's house are opposite to each other. To reach Mansi's house, Rashmi has to go straight towards North-East Therefore, clearly, to go to Rashmi's house Mansi will have to go exactly opposite to North-East and that direction will be South-West.

M = Mansi's House

R = Rashmi's House

Rest of the options is incorrect because of the correctness of option (a).

Directions (Questions 1 to 3): Study the information given below carefully and answer the questions that follow: A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H, while D is 3 km east of G. F is 2 km north to G. I is situated just in the middle of B and C, while E is just in the middle of H and D.

1. Distance between E and G is:

(a) 1 km                                                (b) 1.5 km

(c) 2 km                                                 (d) 5 km

(e) None of these

2. Distance between E and I is:

(a) 1km                                               (b) 2km

(c) 3km                                               (d) 4km

(e) None of these

3. Distance between A and F is:

(a) 1km                                       (b) 1.41km

(c) 2km                                       (d) 3km

(e) None of these

Explanation: The location of the houses is as shown in the adjoining figure. 

1. Option (c) is correct.

Since E lies in middle of H and D, so HE = ED. But HD = 2 km. So, HE = ED = 1 km.

\[\therefore \] Required distance = GE = GH + HE

= (1+1) km = 2 km.

2. Option (a) is correct.

I lies in middle of B and C. So, BI = IC.

But BC = 2 km. So, BI = IC = 1 km.

So, I lies directly above E.

\[\therefore \] Required distance = EI = HB= 1 km.

3. Option (a) is correct.

Since GF = AH = 2 km, so F and A lie in the same line.

\[\therefore \] Required distance = AF = GH = 1 km.