# 12th Class Mental Ability Arrangement Notes - Direction Sense Test

Notes - Direction Sense Test

Category : 12th Class

Direction Sense Test

Concept of Direction: In general we make our concept of direction after seeing the position of the Sun. It is an universal truth that Sun rises in the East and goes down in the West. Thus, when we stand facing sunrise our front is called East, and 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 to make the concept more clear.

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

Concept of Turn

Left turn       =  Anti clockwise turn

Right turn     =   Clockwise turn

Let us understand it through pictorial presentation:

(i) (ii) (iii) (iv) Important Points Regarding Directions

• If our face is towards North, then after left turn our face will be towards West while 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. A dog runs 20 metre towards East and turns right, runs 10 metre and turns to right, runs 9 metre and again turns to left, runs 5 metre and then turns to left, runs 12 metre and finally turns to left and runs 6 metre. Now in which direction the dog is facing?

(a) East                         (b) North

(c) West                         (d) South

(e) None of these

Ans.    (b)

Explanation: The movement of dog can be shown by the following diagram: From the above diagram, it is clear that the dog is facing North.

2.        Suganya moves a distance of 7 m towards South-east, then she moves towards West and travels a distance of 14 m. From here, she moves a distance of 7 m towards North-west and finally she moves a distance of 4 m towards East and stood at that point. How far is the starting point from where she  stood?

(a) 3 m                          (b) 4 m

(c) 5 m                          (d) 10 m

(e) None of these

Ans.    (d)

Explanation: The movements of Suganya are as shown in figure. Clearly, Suganya?s distance from the starting point O is OD

$=(OC-CD)=(AB-CD)=(14-4)m=10\text{ }m].$

3. One day, Raviraj left home and cycled 20 km southwards, turned right and cycled 10 km then turned right and cycled 20 km and finally turned left and cycled 20 km. How many kilometres will he have to cycle to reach his home straight?

(a) 50 km                       (b) 30 km

(c) 40 km                       (d) 60 km

(e) None of these

Ans.    (b)

Explanation: Raviraj starts from home at A, moves 20 km to South upto B. Then he turns right and moves 10 km upto C, then he turns right and moves 20 km upto D, then he turns lefts and moves 20 km upto E.

So, from image it is clear that, if he moves straight, then he will have to move to reach the home.

Now, $AD=BC=10\text{ }km.$

Thus, $AD+DE=10+20=30\text{ }km$

So, he will have to move 30 km to reach the home.

4. Surender went 8 km towards South and then turned to his right and walked 3 km. From this point, he again turned to his right and walked 5 km. In the end he turned to his right again and walked 3 km and then turned to his left and stopped. In which direction is Surender from the starting point?

(a) East                         (b) North

(c) West                         (d) South

(e) None of these

Ans.    (d)

Explanation: The movements of Surender are shown in the diagram given below: It is clear from the diagram that Surender came back on the path (from where he started his journey) and facing the same point from where he started his journey. Thus, Surender is facing towards South direction at the end.

5. A walks 4 km North and turns right and walks 5 km. Then he turns towards South and walks 2 km.  Again he turns towards West and walks 3 km and rests. Again he walks 2 km. How far is A now from  his initial point?

(a) 16 km                       (b) 12 km

(c) 2 km                         (d) 4 km

(e) None of these

Ans.    (c)

Explanation: The situation described in the question is shown in the diagram given below: Thus, the diagram clearly shows that A is at a distance of 2 km from his initial point.

6. Bindu walked 20 metres towards West. Then turning right, she walked 10 metres. Again she turned right and moved 20 metres. In which direction and how far is she from her original position?

(a) North, 50 m              (b) North, 10 m

(c) East, 50 m                (d) South, 10 m

(e) None of these

Ans.    (b)

Explanation: Let I be the starting point and F be the final point. The path followed by Bindu during her movement is shown below: So, Bindu is 10 m away from her original position in North direction.

Concept of Minimum Distance

When a person moves in a straight line from a point A (say) to another point C and then turns to his right or left and again moves in a straight path upto B, he covers a distance of  to reach at point B from the point A.

In this case points A, B and C join to form a right angle triangle. Here the sides AC and BC are called perpendicular and base respectively and the sides AB is called hypotenuse. AC, BC and AB are related by the following formula

$A{{B}^{2}}=A{{C}^{2}}+B{{C}^{2}}$

This important rule is known as ‘Pythagoras Theorem’. The distance AB gives the minimum distance between points A and B. 7. Kunal 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) 5 km North                (b) 5 km South

(c) 5 km East                    (d) 5 km North-East

(e) None of these

Ans.    (d)

Kunal moves 10 km northwards from A upto B, then moves 6 km southwards upto C, turns towards east and moves 3 km upto D as shown below: Then $AC=\left( AB-BC \right)=4\text{ }km$

So, Kunal’s distance from starting point $A=AD=\sqrt{A{{C}^{2}}+C{{D}^{2}}}=\sqrt{{{4}^{2}}+{{3}^{2}}}=5$

So, Kunal is 5 km far from the starting point in North-East direction with reference to starting point.

8. Reeta forgot the way while going to her unders house. She went 2 km South, then turned right and went 2 km west. She then turned right and walked 3 km, and again turned right and walked 1 km to reach her uncle’s house. How far is her uncle’s house from Recta’s house?

(a) 1 km                        (b) 7 km

(c) 2 km                         (d) $\sqrt{2}$ km

(e) None of these

Ans.    (d)

Let R be the Reeta’s house and U represents the uncle’s house. The path travelled by Reeta is shown below: According to Pythagoras theorem, $R{{U}^{2}}=\sqrt{R{{S}^{2}}+S{{U}^{2}}}=\sqrt{{{1}^{2}}+{{1}^{2}}}=\sqrt{2}\,\,km$.

Snap Test

1. A man is facing towards west and turns through $\mathbf{45{}^\circ }$clockwise, again $\mathbf{180{}^\circ }$ clockwise and then turns   through $\mathbf{270{}^\circ }$ anti clockwise. In which direction is he facing now?

(a) West                         (b) North-west

(c) South                       (d) South-west

Ans.    (d)

Explanation: As shown in figure, the man initially faces in the direction OA. On moving $45{}^\circ$ clockwise, the man faces in the direction OB. On further moving $180{}^\circ$ clockwise, he faces in the direction OC. Finally, on moving $270{}^\circ$ anti-clockwise, he faces in the direction OD, which is South-west. 2. I am facing east, I turn $\mathbf{100{}^\circ }$ in the clockwise direction and then $\mathbf{145{}^\circ }$ in the anticlockwise direction.            Which direction am I facing now?

(a) East                          (b) North-west

(c) North                        (d) South-west

Ans.    (b)

Explanation: As shown in figure, the man initially faces towards east i.e., in the direction OA. On moving $100{}^\circ$ clockwise, he faces in the direction OB. On further moving $145{}^\circ$ clockwise, he faces in the direction OC. Clearly, OC makes an angle of $\left( 145{}^\circ -100{}^\circ \right)$ i.e. $45{}^\circ$ with OA and as such points in the direction North-east. 3. Kunal walks 10 kilometers towards North. From there he walks 6 kilometers towards South. Then he walks 3 kilometers towards East. How far and in which direction is he with reference to his starting point?

(a) 5 kilometres West      (b) 5 kilometres North-East

(c) 7 kilometres East        (d) 7 kilometres West

Ans.    (b)

Explanation: The movements of Kunal are as shown in figure $\left( A\text{ }to\text{ }B,\text{ }B\text{ }to\text{ }C\text{ }and\text{ }C\text{ }to\text{ }D \right)$ $AC\text{ }=\text{ }\left( AB-BC \right)=\left( 10-6 \right)\text{ }km=4\text{ }km$

Clearly, D is to the North-east of A.

Kunal’s distance from starting point           $=AD=\sqrt{A{{C}^{2}}+C{{D}^{2}}}$

$=\sqrt{{{4}^{2}}+{{3}^{2}}}=25\,=5\,km$

So, Kunal is 5 km to the North-east of his starting point.

4. Prakash walked 40 metres towards North, took a left turn and walked 20 metres. He again took a left turn and walked 40 metres. How far and in which direction is he from the starting point?

(a) 20 metres East          (b) 20 metres North

(c) 20 metres South         (d) 100 metres South

Ans.    (e)

Explanation: The movement of Prakash are as shown in figure. (A to B, B to C and C to D) 5. A man leaves for his office from his house. He walks towards East After moving a distance of 20 m, he turns South and walks 10 m. Then he walks 35 m towards the West and further 5 m towards the North. He then turns towards East and walks 15 m. What is the straight distance (in metres) between his initial and final positions?

(a) 0                              (b) 5

(c) 15                            (d) Cannot be determined

Ans.    (b)

Explanation: The movement of the man from A to F are as shown in figure. Clearly, $DC=AB+EF$

$\therefore$         F is in line with A.

Also, $AF=\left( BC-DE \right)=5m$

So, the man is 5 metres away from his initial position.

6. A villager went to meet his uncle in another village situated 5 km away in the North- east direction of his own village. Form there he came to meet his father-in-law living in a village situated 4 km in the south of his uncle’s village. How far away and in what direction is he now?

(a) 3 km in the North       (b) 3 km in the East

(c) 4 km in the East         (d) 4 km in the West

Ans.    (b)

Explanation: The villager moves from his village at O to his uncle’s village at A and there to his father-in-law’s village at B. Clearly, $\Delta \,OBA$ is right-angled at B.

So, $O{{A}^{2}}=O{{B}^{2}}+A{{B}^{2}}$

$\Rightarrow \,\,\,\,O{{B}^{2}}=O{{A}^{2}}-A{{B}^{2}}$

$\Rightarrow \,\,\,OB=km=km=3\,km$

Thus, B is 3 km to the east of his initial position O.

7. 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 reaches his destination D. The shortest distance between the starting point and the destination       is

(a) 12 km                       (b) 15 km

(c) 16 km                       (d) 18 km

Ans.    (b)

Explanation: The movements of the person are as shown in figure. Clearly, $AB=3\text{ }km$

$BC=3AB=\left( 3\times 3 \right)\text{ }km=9\text{ }km$,

$CD=SAB=\left( 5\times 3 \right)\text{ }km=15\text{ }km,$

Draw $AE\bot CD$.

Then, $CE=AB=3\text{ }km$ and $\,AE=BC=9\text{ }km$.

$DE=\left( CD-CE \right)=\left( 15-3 \right)km=12\text{ }km$.

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

$AD=\sqrt{{{9}^{2}}+{{(12)}^{2}}}\,km$

$\Rightarrow \,\,\sqrt{225}\,km=15\,km$

$\therefore$      Required distance $=AD=15\text{ }km.$

8. Rohit walked 25 metres towards South. Then he turned to his left and walked 20 metres. He then   turned to his left walked 25 metres. He again turned to his right and walked 15 metres. At what   distance is he from the starting point and in which direction?

(a) 35 metres, East          (b) 35 metres, North

(c) 40 metres, East          (d) 60 metres, East

(e) None of these

Ans.    (a)

Explanation: Option (a) is correct. The movements of Rohit are as shown in figure. Rohit’s distance from starting point $A=AE$

$=\text{ }\left( AD\text{ }+\text{ }DE \right)\text{ }=\text{ }\left( BC+DE \right)=\left( 20+15 \right)m=35\text{ }m$

Also, point E is to the East of A. So, he is in East direction,

9. Sobha was facing East. She walked 20 metres. Then she moved to her left and walked 15 metres. And then turned to her right and moved 25 metres. Again, she turned right and moved 15 metres. How far is she from her starting point?

(a) 25 metres                  (b) 35 metres

(c) 50 metres                  (d) 45 metres

(e) None of these

Ans.    (d)

Explanation: Option (d) is correct.

Shobha turns left after walking 20 metre towards East. Now she walks 15 metre towards North. She turns right towards East again and walks 25 metre further. Finally turning right towards South, she walks 15 metre. The distance moved towards North and towards South is same, i.e., 15 metres. So, Shobha is metre away from her starting point.

10. Raj travelled from a point X straight 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

(e) None of these

Ans.    (a)

Explanation: Option (a) is correct. The movements of Raj are as shown in figure (X to Y, Y to A, A to B, B to C). $\therefore$         Raj’s distance from the starting point $=\text{ }XC=\left( XY-YC \right)=\left( XY-BA \right)=\left( 80-70 \right)m=10m$

11. Mohan starts from point P and reaches point Q at a distance of 6 km, then he turns right and walks 8 km to reach the point R. Then he turns towards East and walks 4 km, then turns left and walks 8 km  and reaches the point T. What is the distance of point T from point P?

(a) 10 km                       (b) 12 km

(c) 14 km                       (d) 26 km

(e) None of these

Ans.    (a)

Explanation: Option (a) is correct. The movements of Mohan are shown in the figure given below: The distance between point P and T is, $PT=PQ+QT=6+4=10\text{ }km$

12. My face is towards South. By turning according to which sequence my face will remain in the same direction?

(a) Left, Right, Left, Right, Left, Left, Right, Right

(b) Left, Left, Right, Right, Left, Right, Left, Left

(c) Right, Right, Right, Left, Left, Left, Right, Right

(d) Right, Left, Left, Right, Left, Left, Right, Left

(e) None of these

Ans.    (a)

Explanation: Option (a) is correct. Thus, by turning according to the sequence given in option (a), my face will remain in the same direction, i.e. in  South.

13. A person started walking towards West and covered a distance of 15 m, he turned right and walked 10 m. Again he turned right and walked 5 m and in the end he turned left and walked 15 m. In which direction this person is now?

(a) North                        (b) South

(c) East                          (d) West

(e) None of these

Ans.    (a)

Explanation: Option (a) is correct. The movement of the person is shown in the diagram given below: He is now towards North.

14. Two buses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 15 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor breakdown, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point?

(a) 60 km                       (b) 65 km

(c) 75 km                       (d) 85 km

(e) None of these

Ans.    (b)

Explanation: Option (b) is correct. Let X and Y be two buses. Bus X travels along the path PA, AB, CD.

Now, $AD=BC=25\text{ }km$

So, $PD=PA+AD=50\text{ }km$

Bus Y travels 35 km upto E.

Distance between two buses, $DE=PQ-\left( PD+QE \right)=\left[ 150-\left( 50+35 \right) \right]=65\text{ }km$

15. X and Y start moving towards each other from two places 200 m apart. After walking 60 m, Y turns  left and goes 20 m, then he turns right and goes 40 m. He then turns right again and comes back to the road on which he had started walking. If X and Y walk with the same speed, what is the distance      between them now?

(a) 20 m                        (b) 30 m

(c) 40 m                        (d) 50 m

(e) None of these

Ans.    (c)

Explanation: Option (c) is correct. Clearly Y moves 60 m from Q upto A, then 20 m upto B, 40 m upto C and then upto D. So, $AD=BC=40\text{ }m$

Thus, $QD=AD+AQ=\left( 60+40 \right)m=100\text{ }m$

Since X and Y travel with the same speed, X will travel with the same along the horizontal as Y travels in the same            time.

Now, total distance travelled by $Y=\left( 60+20+40+20 \right)=140\text{ }m$

So, X also travels 140 m upto A.

Distance between X and $Y=AD=QD-AQ=(100-60)\,m=40\,m$

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##### Notes - Direction Sense Test

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