Distance and Directions

Questions based on Distance and Directions can only be solved if the students have a full grasp of directions. The First thing to remember is that there are four directions: These directions are given under.

Directions

JOINT DIRECTIONS

For the person standing in the area falling between

• North and east direction is called North₇East.
• The area between South and East is called South-East
• The area between North and West is called North-West
• Similarly, the area between South direction and West direction is called South-West.

• Every turn taken clockwise (CW) means taking a right turn and Anti-clock wise (ACW) turn means taking left turn.

RULES FOR DISTANCE AND DIRECTION

Turning By 90⁰

Turning       45°

 

For Example

FINDING OUT DISTANCE

The student is generally expected to find out the distance between the starting point and the destination point. To find out the shortest distance between the two points i.e., starting point and the destination point. should draw the diagram, which shows actual path followed by the person, along with the distance travelled by him. Finally, the starting point and destination are joined by a straight line and distance is observed. For this we use Pythagoras theorem which is as follows:

SOLVED EXAMPLES

Direction (1-3): Read the following information carefully and answer the given questions.

A @ B means A is to the north of B at a distance of either 7m or 12m
A # B means A is to the west direction of B at a distance of either 5m or 14m
A $ B means A is to the south direction of B at a distance of either 7m or 12m
A & B means A is to the east direction of B at a distance of either 5m or 14m
A @& B means A is to the north-east of B
A $& B means A is to the south-east direction of B

1. Statement

A@B, B#C, C$D@&A, D#E@F@&C, F@G$&C, G&H$C

In which direction is B with respect to H?
(A) North (B) East (C) North-East (D) North-West (E) None of these

2. If distance between B and C is same as the distance between D and E and this distance is less than the distance between A and B. Point X Which is 5m north of point A then what is the total distance between X and E?
   (A) 10 m (B) 28 m (C) Either a or b (D) 5 m (E) 14 m
3. What is the total distance between E and G?
   (A) 12 m (B) 17 m (C) 19 m (D) 21 m (E) None of these

1. Correct option is: D 2. Correct option is: A 3. Correct option is: C

Ex.1. A man is facing west. He turns 45° in the clockwise direction and then another 180° in the same direction and then 270° in the anti-clockwise direction. Which direction is he facing now?

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

Sol. Clearly, then man initially faces in the direction OA. On moving 45° clockwise, he faces in the direction OB. On further moving 1 80° clockwise, he faces in the direction OC. Finally, on moving 270° anti-clockwise, he faces in the direction OD, which is South-West. Hence, the answer is (d)

Ex.2. Sapna moved a distance of 75m towards the north. She then turned to the left and walking for about 25m, turned left again and walked 80 m. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?

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

Sol. Sapna started from A, moved 75m up to B, turned left and walked 25m up to C. She then turned left again and moved 80m up to D. Turning to the right at an angle of 45°, she was finally moving in the direction D i.e., South-West.  Hence, the answer is (e).

PRACTICE TEST-1

1. Aman is facing towards west and turns through 45° clockwise, again 180° clockwise and then turns through 270° anti clockwise. In w hich direction is he facing now?

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

2. A river flows West to East and on the way turns left and goes in a semi-circle round a hillock, and then turns left at right angles. In which direction is the river finally flowing?

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

3. L am standing at the centre of a circular field. I go down south to the edge of the field and then turning left I walk along the boundary of the field equal to three-eighth of ifs length. Then I turn west and 90° right across to the opposite point on the boundry. In which direction am I from the Starting point?

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

 4. A man leaves for his office from his house. He walks towards east. After moving 20m, he turn South and walks 10m. Then he walks 35m towards the west and further 5m towards the north. He then turns towards east and walk 15m. What is the straight distance (in meters) between his initial and final position?

(a) 0                 (b) 5                 (c) 10                           (d) cannot be determined      (e) none of these

5. Maya starts at point T, walks straight to point U which is 4Ft away. She turns left at 90° and walks to W which is 4ft away, turns 90° right and goes 3ft to P, turns 90° right and walks 1ft to Q, turns left at 90° and goes to V, which is 1 ft away and once again turns 90° right and goes to R, 3ft away. What is the distance between T and R?

(a) 4 ft             (b) 5 ft             (c) 7 ft              (d) 8ft

6. A villager went to meet his uncle in another village situated 3 km away in the North direction of his own village. From there he came to meet his father-in-law living in a village situated 4 km in the East of his uncle’s village. How far away and in what direction is he now from his house?

(a) 3 km in the northeast                    (b) 5 km in the northeast

(c) 4 km in the northeast                    (d) 4 km in the southeast

7. Starting from a point P, Sachin walked 20 m towards south. He turned left and walked 30m. He then turned left and walked 20m. He again turned left and walked 40 m and reached a point Q. How far and in which direction is the point Q from the point P?

(a) 20 m west              (b) 10 m east   (c) 10 m west              (d) 10 m north      (e) none of these.

8. Rahul started from his house and walked 3 km east, then he turned right and walked 2 km, then again, He turned left and walked 1 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school. What is the minimum distance between Rahul’s house and his school?

(a) 12km                      (b) 9km            (c) 6km                                    (d) 3km            (e) 5km

9. If South-East become North, North-East becomes West and this trend is continued, what will be the original West becomes?

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

10. Ria started from her house and goes 80 m in North direction, then she turns right, walks another 30m, turns right again and walks 40m. How for is she now from her home? 

(a) 50m                        (b) 80m           (c) 40m            (d) 70m           (e) None

11. Gouravy starts from his house for school. He walks 1 km towards east, turns right and walks 300m, then again turns right, moves a little away and turns left and after walking some 500 m reaches the school. In which direction is his school from his house?

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

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

(a) 65 kms                   (b) 75 kms                   (c) 80 kms                    (d) 85 kms

13. P, Q, R, S, T,  U, Y, W are sitting around a round table in the same order, for group discussion at equal distances. Their position is clockwise.  If V sits in the North, then what will be the position of S?

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

14. The town of Paranda is located on green lake. The town of Akram is west of Paranda. Tokhada is east of Akram but west of Paranda. Kakran is east of Bopri but west of Tokhada and Akram. If they are in the same district, which town is the farthest west?

(a) paranda     (b) Kakran                   (c) Akram                    (d) Bopri

15. Five boys are standing ina row facing east. Deepak is to the left of Sameer, Tushar and Shailender. Sameer, Tushar and Shailender are to the left of Sushil.  Shailender is between Sameer and Tushar. If Tushar is fourth from the left, how for is Sameer from the right?

(a) First            (b) Second       (c) Third           (d) Fourth        (e) Fifth

Directions (16-18): Read the following information carefully and answer the following questions given below:

Bhavya is 5 km to the west of Ankit. Chetan is 5 km to the north of Bhavya.  Elena is 5 km to the south of Diamond. Chetan is 10 km to the west of Diamond. Farheen is 2.5 km to the west of Elena. Gaurav is 10 km to the north of Farheen; Gaurav is 5 km to the east of Hishi.

16. What is the shortest distance between Hishi and Farheen?

17. What is the direction of Garav with respect to Bhavya?

(a) North         (b) Northeast (c) South          (d) Southeast  (e) None of these.

18. What is the total distance between Bhavya and Hishi?

 (a) 26km         (b) 24 km         (c) 25 km         (d) 27 km         (e) 22.5 km

Directions (19-20): Read the following information carefully, and answer the following questions given below.

Kritika is 25km north of Pritika. Drishti 20km south of Srishti. Drishti is 15km west of Urvashi. Vaishnavi is 8km north of Richi. Vishi is 20km south of Urvashi. Richi is 15km east of Kritika. Srishti is 8km west of Vaishnvi.

19. If Ridhi is midpoint of Kritika-Pritika, how far is Ridhi with respect to Pritika?

(a) 12km          (b) 13 km                     (c) 12.5km       (d) 25 km         (e) None of these.

20. If Radhika starts walking from Drishti and walks 6km in cast direction and stop at point Y, Piya starts walking from Urvashi and walks 3km in west direction and stop at point Z. What is shortest distance between Y and Z?

(a) 5km            (b) 7 km           (c) 8km                        (d) 6km                        (e) None of these.

ANSWERS

l. (d)     2. (b)    3. (c)    4. (b)    5. (d)    6. (b)    7. (c)    8. (e)    9. (b)    10. (a)

11. (b)    12. (a) 13. (d) 14. (d) 15. (d) 16. (a) 17. (b) 18. (e) 19. (c) 20. (d)

Directions (1 to 2): Study the information below carefully and answer. the question that follow.:

On a playing ground, Dinesh, Kunal, Nitin, Atul, and Prashant are standing as described below facing the North.

(i) Kunal is 40 m to the right of Atul.

(ii) Dinesh is 60 m to the South of Kunal.

(ili) Nitin is 25 m to the West of Atul.

(iv) Prashant is 90 m to the North of Dinesh.

1. Who is to the north-east of the person who is to the left of Kunal?

(a) Dinesh        (b) Nitin           (c) Atul |          (d) Either Nitin or Dinesh        (e) None of these

2. If a boy walks from Nitin, meets Atul followed by Kunal, Dinesh and then Prashant, how many meters has he walked if he has travelled the straight distance all through?

(a) 155m          (b) 185m         (c) 215m          (d) 245m         (e) none of these

Directions (3 to 4): Read the information carefully and answer the questions given below it.

(i) Six flats on a floor in two rows facing North and South are alloted to P, Q, R, S, T and U.

(ii) Q gets a North facing flat and is not next to S.

(iit) S and U get diagonally opposite flats.

(iv) R, next to U, gets a South facing flat and T gets a north facing flat.

3. Which of the following combination get South facing flat?

(a) QTS        (b) UPT   (c) URP   (d) Data inadequate                 (e) None of these

4. Whose flat is between Q and S ?

(a) T                 (b) U                (c) R                 (d) P                 (e) Data inadequate

5. A man performing yoga with his head down and legs up, his face is towards the west. In which direction will his left hand be ?

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

6. Anuj started walking positioning his back towards the Sun. After some time, he turned left, then turned right and then towards the left again. In which direction is he going now?

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

7. One morning after sunrise a boy walks a while facing towards the sun he turns to his right and continues to walk. Later, he turns left and finally, turnig to his right, he stops. Which direction is he facing now?

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

8. A man travels 7 kms towards east, then he turns left and travels 8 kms, again he turns left and travels 10 kms. Finally, he turns left and travels 2 kms. In which direction is he from his starting point?

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

9. A watch reads 4:30. If the minute hand points towards the east, in what direction will be hour hand point ?

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

10. P, Q, R and S are playing a game of Carrom. PR and SQ are patners. S is to the right of R who facing West, Q is facing?

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

Direction (11-12): Read the following information carefully, and answer the following questions given below.

On a playing ground Sanchi, Rakhi, Preety, Simu and Rahul are standing as described below facing the North,

(i) Rakhi is 100 mts to the left of Simu.

(ii) Sanchi is 60 mts to the North of Rakhi.

(iii) Preety is 40 mts to the East of Simu.

(iv) Rahul is 80 mts to the South of Sanchi.

11. If Neha walks from Preety, meets Simu followed by Rakhi, Sanchi and then Rahul, how many mts has she walked if she has travelled the straight distance through the given points?

(a) 220                         (b) 250                         (c) 280                         (d) 230             (e) None of these

12. What is the distance (in km approximately) between Preety and Rahul if travelled straight distance through the given points?

(a) 130                         (b) 220                         (c) 150                         (d) 140             (e) 160

Direction (13-16): Read the following information carefully and answer the questions given below.

Kavita starts walking from his house. She walks to the east for 10 kilometres to reach the Shop and in the midway, she passes a gym. If she returns to the gym and walks to the south for 3 kilometres, she reaches a cinema. If at the cinema she turns to the right and walks 2 kilometres, she reaches the school, but if she walks 5 kilometres to the southwest of the cinema, she reaches a mall. From the mall, she walks 16 kilometres to the east to reach the park. There is a stadium 5 kilometres to the northwest of the park. Distance between Stadium and cinema is 10 km. If she walks 5 kilometres to the south from the mall, she reaches the pool. At the pool, if she turns to the left and walks 5 kilometres, she reaches IBT. If she goes 3 metres towards East from mall, she is to the south of cinema.

13. Kavita’s house is at which direction with respect to IBT?

(a) South         (b) North         (c) North-East (d) North-West                       (e) None of these

14. What is the minimum distance of Cinema from the Shop (in kilometres)?

(a) 5                 (b) 10               (c) 12               (d) 2.5              (e) 5.8

15. What is direction of Cinema with respect to IBT?

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

16. If Kavita is standing at the school facing to the West, in which direction does she needs to turn before starting to walk for reaching the mall through minimum possible path?

(a) Right          (b) Left                        (c) 2 times left                         (d) 2 times right                        (e) None of these

Directions (17-19): Read the following information carefully. And answer the following questions given below.

Janhvi starts from point PR Walks 21km towards the west, turn towards left and walks 10 km. She then takes right turn, walks 12 km, and stops.

Riva starts from the same point P, walks 20 km towards the North, takes a left turn and walks 25 km before stopping. After that Riya takes left turn and walks 20 km and react point Q. Janhvi walks 4 km from the point where she stopped in a straight line in the same direction which she faced when she stopped and reaches point R.

17. How far and in which direction is Riya with respect to Jahnvi? (approx…)

(a) 16 km towards North-east                        (b) 15.6 km towards North-east

(c) 14.6 km towards North-west                    (d) 15.6 km towards South-east q

(c) 15.6 km towards North 4

18. If Janhvi takes a right turn from the point where she stopped, walks 10 km and again stops, how far would she be from the position where Riya stopped?

(a) 4km            (b) 2km                        (c) 12km                      (d) 18 km         (e) 14km

19. What is total distance covered by Riya?

(a) 60 km         (b) 65 km                     (c) 55 km         (d) 75 km         (e) None of these

Directions (20-22): Study the information given below carefully and answer the questions that follow.

Point Bita is 15m to the east of Point Alpha and 10m to the South of Point Coma. Point Dell is 10m to the east of Point Coma and 10 m to the north of Point Ela. Point Foil is 10 m to the southwest of Point Ela such that Ela, Bita, and Foil forms a right-angled triangle. Point Gama is 20m to the south of Point Hill and 20 m to the east of point Foil.

20. Point Gama is in which direction with respect to point Bita?

(a) Southeast              (b) North         (c) South-west             (d) East            (e) None of these

21. Point Foil is in which direction with respect to point Coma?

(a) Southeast              (b) North         (c) South          (d) East                        (e) North East

22. If a person moves 10 m towards East from Point Bita then he reaches which point?

(a) Alpha          (b) Ela                         (c) Coma                      (d) Gama                     (e) Hill

ANSWERS

1. (e)    2. (c)    3. (c)    4 (a)     5. (a)    6 (A)    7. (b)    8. (a)    9.(d)     10.(d) 11. (c)   12. (e)        13. (d) 14. (e) 15. (c) 16. (b) 17. (b) 18. (c) 19. (b) 20. (a)  21. (c) 22. (b) (b)

PRACTICE TEST-III:

Directions (1-3): Read the following information carefully and answer the questions given below it:

i. M?N means N is to the right of M at a distance of two metre.

it. M*N means N is to the North of M at a distance of two metres.

il. M+N means N is to the left of M at a distance of two metre.

iv. M%N means N is to the South of M at a distance of two metres.

v. In each of the following questions all persons face North.

1. If P%Q+R*S then S is in which direction with respect to P?

a) South-east b) Past                         c) North           d) West                       e) None of these

2. If X?R%Y?Z then Z is in which direction with respect to R?

a) North           b) West           c) South-east   d) South-west e) None of these

3.If T ? U +  V* W, then V is in which direction with respect to T?

a) North           b) South          c) East d) North-East              e) None of these

Directions (4-8): Read the following information carefully and answer the questions given below it:

Nine cars — C1, C2, C3, C4, C5, C6, C7, C8 and C9 were located at some distance from cach other in a parking area. C3 was 16m $ to that of C2.  C1 was 6m % of that of C2 and C8 was 12 m # of that of C1.  C7 was 8 m @ of that Of C3 while C4 was 24m $ of that of C7 and C6 was 12 m % of that of C7. C9 was situated just in the middle of C2 and C3 while C5 was just in the middle of C8 and C4.

Here, % means North, # means South, $ means East and @ means West

Note: If two symbols are given simultaneously then both the directions will be considered.

For example,

X%$Y means Y is to the North-East of X

Y%$X means X is to the North-East of Y

4. Which of the following is/are true about C2?

A. C9@C2%@C6                     B. C2#@C7                  C. C2#$C4

(a) All are true             (b) Both A and B          (c) Only A        (d) Both B and C          (e) Only C

5. What is the direction of C4 with respect to C6?

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

6. What is the shortest distance between car C2 and car C6?.

(a) 12m            (b) 10m           (c)9m               (d) 11m           (e) None of these

7, Which of the following cars lie in the straight line?

(a) C7 and C2   (b) C3 and C8 (c) C7 and C5   (d) C5 and C1              (e) None of these

 8. What is the direction of C5 with respect to C9?

(a) South         (b) South – West          (c) North – East                        (d) North         (e) None is true

 Directions (9-11): Read the information given below carefully and answer the following questions. The data given are in some coded format, throughout and proceed further.

@ — North      $ — Either 2 metres or 7 metres

% — South      # — Either 4 metres or 9 metres

* — Fast          © — West

i.e., A@ B means A is to the North of B.

A %* B means A is Southeast of B.

A $B means A is either 2 metres or 7 metres from B.

A %# B means A is South of B and with either 4 or 9 metres.

Point X is to the west of point P with distance of 4 metres.

Set-1:                                                   Set-2:

I. P@$Q                                               I.S ©$ U

II. Q *#R                                              Il. O %#S

III. R %# T                                            III. O *$ T

IV. T %© X                                           IV. U@P

Distance between point 11 and P is greater than distance between point X and P.

9. What is the distance between Q and U?

(a) 9m              (b) 11 m          (c) 13m                        (d) 15m                       (e) None of these

10. Which of the following will be true as per the given data?

(a) R@© P       (b) P %© S       (c) X %* U        (d) O @© Q     (e) None of these

11. If B %S X and point B lies in line with R and Q, then which of the following will be true?

(a) B©# Q        (b) B *$ Q        (c) R*$ B          (d) Both (a) and (c)       (e) None is true

Directions (12-14): Read the direction carefully and answer the questions that follow:

a @  b means a is 7km left of b

a # b means a is 4km right of b

a % b means a is 6km north of b

a $ b means b is 5km south of a

12. By adding the equations ‘P $ Q % R’ and ‘Q @ S’, what is the direction of S with respect to R?

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

(e) Can’t be determined

13. What is the diagrammatical representation of the equation E # J @ 0 % T?

14. Consider the equation A @ Q % R and R # S. If S moves 6km from his/her position towards nod then what is the distance between A and S (Assume all are facing north)?

(a) 2 km           (b) 3 km           (c) 4km                        (d) 5km            (e) 6 km

ANSWERS

1. (d)   2. (c)    3.(c)     4.(a)     5. (e)    6. (b)   7. (c)    8. (a)    9. (c)    10. (d) 11. (a)  12.(c)   13.(a)   14.(b)