19 Direction and Distance (English).pdf

DIRECTION AND DISTANCE 19 DIRECTION AND DISTANCE 1. Ashok went 8 kms. South and turned west and 9. Shyam walked 6 meters towards East, then took a walked 3 Kms, again he turned north and wal...

DIRECTION AND DISTANCE 19 DIRECTION AND DISTANCE 1. Ashok went 8 kms. South and turned west and 9. Shyam walked 6 meters towards East, then took a walked 3 Kms, again he turned north and walked 5 right turn and walked a distance of 9 meters. He Kms. He took a final turn to east and walked 3 Kms. then took a left turn and walked a distance of 6 In which direction was Ashok from the starting point? meters. How far is he from the starting point? (A) East (B) North (C) West (D) South (A) 15 meters (B) 21 meters 2. Starting from a point P, Sachin walked 20 m towards (C) 18 meters (D) CND South, he turned left and walked 30 m. He then 10. Vimal starts from point P and walks toward South turned left and walked 20 m. He again turned left and stops at point Q. He now takes a right turn fol- and walked 40m and reached a point Q. How far and lowed by a left turn and stops at point R. He finally in which direction is the point P from the point Q? takes a left turn and stops at point S. If he walks 5 (A) 20 m West (B) 10 m West Kms. before taking each turn, towards which direc- (C) 10 m East (D) 10 m North tion will Vimal have to walk from point S to reach (E) None of these point Q? 3. Roy walked 2 km. to East, then turns North-west and (A) North (B) South walks 3 Km. Then he turned South and walked 5 Km. (C) West (D) East Then again he turns west and walked 2 Km. Finally (E) North-West he turned North and walked 6 Km. In which direction 11. Imagine that you are walking towards South. After is he from the starting point? sometime you turn left. Then again you turn left. Af- (A) South-West (B) South-East ter that you turn right and once again turn to the (C) North-West (D) North-East right. In which direction you are walking now? (E) None of these (A) East (B) West 4. Vimal faces towards north and turning to his right, he (C) South (D) North walked 25 meters. He then turns to his left and walks 30 (E) None of these meter. Next, he moves 25 meters after turning to his right. 12. M walked 20 meters towards west, turned left and He then turns to his right again and walks 55 meters. walked 20 meters, then he turned right and walked Finally he turns to the right and moves 40 meters. In 20 meters and again turned right and walked 20 which direction is he now from his starting point? meters. Now, how far is M from his starting point? (A) South-West (B) South (A) 40 m (B) 50 m (C) North-West (D) South-East (C) 80 m (D) Data inadequate 5. Q walked 20 meters towards west and took a left turn 13. If North-east becomes West and South-east becomes and walked 20 meters. He then took a left turn and North then what will West become? walked 20 meters and again took a right turn and walked (A) South-East (B) North-East 20 meters. How far is Q now from the starting point? (C) South (D) North-West (A) 40 meters (B) 50 meters 14. If M is in the south of B and B is in the west of N, (C) 80 meters (D) Data inadequate then in which direction is N from M? (E) None of these (A) North (B) East 6. Tom walked 10 miles from point P towards the east. (C) North-East (D) South-West He then took right turn and walked 5 miles and tak- 15. Vimal walks 20 m towards east. He then turns left ing another right turn walked again for another 5 and walks 10 meters. He again turns left and walks miles. In which direction is point P from where Tom 20 meters. How far is he from his starting point? is standing now? (A) 10 meters (B) 50 meters (A) South-East (B) North-West (C) 40 meters (D) 20 meters (C) North-East (D) CND 16. Manish starts walking towards East and walked 30 7. Amit walked 10 Kms. towards North. From there he meters, then he turned right and walked 50 meters turned back and walked 6 Kms. towards South. Then and he again turned left and walked 40 meters. Again he walked 3 km. towards East. How far was he from he turned left and walked 50 meters. Now, how far is the starting point? he from his starting point? (A) 8 Km. (B) 5 Km. (A) 170 m (B) 70 m (C) 7 Km. (D) 6 Km. (C) 120 m (D) 110 m (E) None of these 17. A walks 10 m North, then he turns right and walks 8. Seema walks 1 Km. to east and turns right and walks 10 m. And then turning left each time, he walks 5m, another 1 Km. and then turns left and walks 2 Km. 15m and 15m respectively. Now, how far is he from and again turning to her left travels 5 Km. How far is his starting point? Seema from her starting point? (A) 5 m (B) 10 m (A) 8 Km. (B) 5 Km. (C) 7 Km. (D) 6 Km. (C) 15 m (D) 20 m (E) None of these PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE 18. Navin walked 30 meters towards East, then he turned 26. Nitu starts from point T, walks straight to point U right and walked 20 meters. Again he turned right and which is 4 Ft away. She turns left at 90° and walks to walked 30 meters. How far is he from his starting point? W which is 4 Ft away, turns 90° right and goes 3 Ft to (A) 30 m (B) 80 m (C) 50 m (D) 20 m P, turns 90° right and walks 1 Ft to Q. Again turns (E) None of these 90° left and walks 1 Ft to V. Finally turns 90° right and walks 3 Ft to reach R. Then what is distance be- 19. Shailesh walks 20 meters towards south. He then tween T and R? turns left and walks 30 meters. After that he turns right and walks 10 meters. Then again he turns right (A) 4 Ft (B) 5 Ft (C) 7 Ft (D) 8 Ft and walks 40 meters. After this he turns right and 27. A person starts from a point A and travels 3 Km east- walks 30 meters. Now he stops. Now, in which direc- wards to B and then turns left and travels thrice that tion is he from his starting point? distance to reach C. He again turns left and travels five (A) South-West (B) West times the distance he covered between A and B and reaches his destination D. The shortest distance be- (C) North-West (D) Starting Point tween the starting point and the destination is: (E) None of these (A) 12 Km (B) 15 Km (C) 16 Km (D) 18 Km 20. Mukesh walked 20 meters towards west, turned right 28. Pran and Khan start from their office and walk in op- and walked 30 meters, again he turned right and walked posite direction, each travelling 10 Km. Pran then turns 20 meters. How far was he from his starting point? left and walks 10 Kms. While Khan turns right and (A) 70 m (B) 40 m (C) 30 m (D) 50 m walks 10 Km. How far are they now from each other? (E) None of these (A) 0 Km (B) 5 Km 21. Seema says to Suresh that she is going to the North (C) 10 Km (D) 20 Km direction to hide, but she went 2 Km. east from there29. Ram is facing North-West and he turns in clockwise and then 3 Km. towards south and again 2 Km. to- direction by 90°, then 180° in the anti-clockwise di- wards west and then again same distance towards rection and turns another 90° in the same direction. the starting place. Now, in which direction is Seema Which direction is he facing now? from her hiding place? (A) South (B) West (A) North (B) South (C) East (D) South-East (C) West (D) East 30. If A is to the South of B and C is to the East of B and (E) None of these D is to the South of C at equal distance, then who is 22. A man is facing west. He turns 45° in the clockwise to the South-East of B? direction and then another 180° in the same direc- (A) A (B) B tion and then 270° in the anticlockwise direction. (C) C (D) D Which direction is he facing now? 31. A man started to walk East. After moving a distance (A) South (B) North-West he turned to his right. He turns right and moving a (C) West (D) South-West little distance again turned in the end to his left. In 23. A man is looking for his friend. He went 90m in the which direction was he going now? east before turning to his right. He went 20m before (A) North (B) South turning to his right again and goes further to look for (C) East (D) West his friend at his uncle's place 30m from this point. 32. If A is 50 meters North-West of B and C is 50 meters His friend was not there, from there he went 100 m to North-East of B and D is 50 meters South of B then north before meeting his friend in a street. How far who is in the East direction of A? did the man meet his friend from the starting point? (A) A (B) B (C) C (D) D (A) 80 meters (B) 100 meters 33. K is P's neighbor and he stays 400 meters away toward (C) 140 meters (D) 260 meters east. N is K's neighbor and resides 400 meters away (E) None of these towards North. S is N's neighbor and he stays 400 m to 24. A rat runs 20' towards East and turns to right, runs 10' west. If distance between S and P is also 400 meters, and turns to right, runs 9' and again turns to left, runsThen who stays in the South-East direction of S? 5' and then turns to left, runs 12' and finally turns to (A) S (B) P (C) N (D) K left and runs 6' Now, which direction is the rat facing? 34. After sunrise Sudhir faces the Sun and walks for one (A) East (B) West Kilometer. Then he turns right and walks for two kms. (C) North (D) South Then he turns right again and walks for one Km. In 25. Guriya moved a distance of 75 meters towards the which direction is Sudhir from his starting point? north. She then turned to the left and walking for about (A) South (B) North 25 meters, turned left again and walked 80 meters. (C) East (D) West Finally, she turned to the right at an angle of 45°. In 35. If A stands on his head with his face towards north, which direction was she facing now? in which direction will his left hand point? (A) North-East (B) North-West (A) North-East (B) North (C) South (D) South-West (C) East (D) West PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE 36. Gandhinagar is to the East of Ambedkar Nagar. 43. Nidhi travelled 5 km. towards North and turned right Subhashnagar is to the North of Gandhinagar. and walked 10 km. and turned left and walked 5 km. Gandhinagar is to the North of Bharatnagar. In which Finally she turned left and walked 10 km. Now in direction is Bharatnagar to Subhashnagar? which direction she is moving? (A) South (B) East (A) East (B) South (C) North (D) West (C) West (D) North 44. In a clock at 12:30 P.M. hours hand of a watch is in 37. Radhika went 50 meter south from her house then eastward direction and minute hand of a watch is in turned left and went 20 meter, then turning to north west. In which direction hours hand of watch will be she went 30 meter. In which direction is her home at 2:45 P.M.? from this point? (A) South-East (B) South (A) North (B) South-West (C) South-West (D) North (C) South-East (D) North-West 45. A clock shows 4:30. P.M. If minute hand toward east 38. Molly travelled from point A to point B which is 5 feet. than in which direction will be hours hand? He then travelled 6 feet to his right and then turned to (A) North-East (B) South-East left and went 4 feet. Finally he again went 6 feet to his (C) North-West (D) North left. How far is he from the point B now? 46. If South-East becomes North, North-East becomes (A) 10 feet (B) 6 feet west and so on. Then what will become west? (C) 9 feet (D) 4 feet (A) North-East (B) North-West 39. Arun walks to north 30 meter, moves left and walks (C) South-East (D) South-West 40 meter. He again turns left and walks 30 meter. (E) South He finally turns left and walks 50 meter. Now how far Arun is from the starting point? 47. If South-East is called East, North-West is called west, South-West is called South and so on. Then what will (A) 50 meter (B) 40 meter be called North? (C) 90 meter (D) 10 meter (A) South-East (B) North-East 40. Balu's house is 300 meter away from that of Sam. (C) East (D) South Balu stays 300 meters South West of Sam's house. Raju resides 600 meters North East of Balu. Then 48. Five villages P,Q,R,S and T are adjacent to each other. where is the position of Sam's house in relation to P is west of Q,S is East of T. R is South of P.T is Raju's ? North of Q. In which direction is R from S? (A) North-East (B) South-East (A) North-East (B) South-East (C) North-West (D) South-West (C) South-West (D) CND 41. Rahul put his Time piece on the table in such a way (E) None of these that at 6 P.M. hour hand points to North direction. 49. Q travelled towards East. M travelled towards North. In which direction will minute hand point at 9:15 S and T travelled in opposite direction. T travelled right P.M.? to Q. Which statement is definitely true in following (A) South-East (B) South sentence? (C) North (D) West (A) M and S are travelling in opposite direction 42. Sunil walks toward east from point A. He turns toward (B) T travelled towards West right at point B and covered same distance which he (C) T travelled towards North traveled in east direction. Now he turned left and cov- (D) M and S travelled in same direction ered same distance. Finally he turns left and covered (E) None of these same and stopped at point C. How many times is the 50. M is East of D.K is West of F and F is South of D. In distance between A and C to that of between A and B? which direction is M from K? (A) Cannot be determined (B) Two (A) South-West (B) North-West (C) Three (D) None of these (C) North-East (D) South-East (E) Data inadequate EXERCISE 1. (D) 6. (B) 11. (C) 16. (B) 21. (B) 26. (D) 31. (B) 36. (A) 41. (D) 46. (C) 2. (C) 7. (B) 12. (A) 17. (A) 22. (D) 27. (B) 32. (C) 37. (D) 42. (B) 47. (B) 3. (C) 8. (B) 13. (A) 18. (D) 23. (B) 28. (D) 33. (D) 38. (D) 43. (D) 48. (C) 4. (D) 9. (A) 14. (C) 19. (B) 24. (C) 29. (D) 34. (A) 39. (D) 44. (B) 49. (D) 5. (A) 10. (A) 15. (A) 20. (C) 25. (D) 30. (D) 35. (C) 40. (D) 45. (A) 50. (C) PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE SOLUTION 1. A 6. 10 miles P 3 km 5 miles B 5 km 8 km Q 5 miles Starting Point = P Ending Point = Q 3 km Starting Point = A The direction of Point P from Q (  ) = North-West Ending Point = B 7. B Direction of Point B from Point A (  ) = South 6km 2. 40 m 10 km 3km Q P C D 20 m 20 m A Starting Point = A 30 m Ending Point = D PQ = 40-30 = 10 m AC = AB-BC Direction of point P from point Q ( ) = East = 10 - 6 = 4 km  10m, East In  ACD 3. B AD² = AC² + CD² AD² = 4² + 3² AD² = 25 AD = 5 3 km  Amit was 5 km away from starting point. 8. B 6 km A 2 km 5 km 1km C A 5km 2 km 1km Starting Point = A Ending Point = B 2km Direction of Point B from A (  ) = North-West Starting Point = A Ending Point = B 4. 25m AC = 1+2 = 3 km BC = 5-1 = 4 km 25m 55m In  ABC A 30m AB² = BC² + AC² AB² = 4² + 3² = 25 B 40m AB = 5 km Starting Point = A  Seema is 5 km away from starting point. Ending Point = B 9. A 6m The direction of Point B from A (  ) = South-East 9m 5. 20m A B C 6m Starting Point = A 20m Ending Point = B AC = 9m 20m 20m BC = 6+6 = 12 m In  ABC B AB² = AC² + BC² Starting Point = A AB² = 9² + 12² = 225 Ending Point = B AB = 15 m AB = 20+ 20 = 40 m  Shyam is 15 m away from starting point. PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE 10. 17. 15m P E F 5m 5km 10m D C 5km 15m Q 10m 5km B A S Starting point = A R 5km Ending point = B The direction of point Q from S (  ) = North AB = EF - CD = 15-10 = 5 m 11. Initial Direction: (South) 18. 30m Left A Left 20m Right Right B 30m Final direction South Starting point = A 12. Ending point = B B 20m A AB = 20 m 19. B A 20m 20m 20m 20m Starting Point = A 30m 30m Ending Point = B 10m AB = 20+20 = 40 m 40m 13. North-East + 135° anticlockwise = West Starting point = A  West + 135° anticlockwise = South-East Ending point = B 14. B The direction of B from A (  ) = West N 20. 20m B 30m A M 20m The direction of N from M (  ) = North-East Starting point = A Ending point = B 20m D AB = 30 m 15. B He is 30m away from A. 10m 21. Hiding place 20m A C 2km Starting Point = A A Ending Point = B B 3km AB = CD = 10 m 2km  He is 10m far from A. 30m 2km 16. A B Starting point = A Ending point = B 50m 50m The direction of B from her hiding place (  ) = South 22. Initial direction-(West) 40m 45° clockwise 270° anti-clockwise 180° clockwise 225° clockwise Starting point = A 270° anti-clockwise 45° anti-clockwise Ending point = B AB = 30+40 = 70 m 45° anticlockwise from west = South-West PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE 23. B 28. Khan Pran 90m C 10km 10km A Office 100m 20m 10km 10km The distance between Pran & Khan = 10 + 10 = 20 km 30m Starting point = A 29. Initial direction-(North-West) 90° clockwise 270° anti-clockwise Ending point = B 180° anti-clockwise 90° clockwise BC = 100-20 = 80m 90° anti-clockwise 180° anti-clockwise AC = 90-30 = 60 m In  ABC 180° anticlockwise i.e. opposite direction AB² = BC² + AC²  Opposite of North-West = South-East AB² = 80²+60² = 10000 30. B C AB = 100m  The man met 100 m away from the starting point. 24. Initial Direction: (East) A D Right Right Point D is to the South-East of B. Left 31. Initial Direction: (East) Left Left Right A left turn from East = North Right Left 25. Initial Direction: (North) A right turn from east = South Left 180° Left Left 45° Right 32. 45° Right A C 135° left = 135° anti-clockwise North+135° anticlockwise = South - West 50m 50m 26. B V 3ft R 1ft 50m P 1ft D Q 3ft C is in the east of A. W U 33. 400m 4ft 4ft S N T 400m 400m TR = TU + PW + VQ P K 400m = 4 + 3 + 1 = 8 ft NOTE: We considered North, initial direction. K stays in South-East of S 27. D E C 34. 1km A 15km 2km 9km B 1km The sun is in the east in the morning. A 3km B Starting Point = A ED = 15–3 = 12 km Ending Point = B AE = BC = 9 km The direction of B from A (  ) = South In  ADE AD² = ED² + AE² 35. In normal position, the direction of A's face  oppo- AD² = 12² + 9² = 225 site of North = South AD = 15 km The left of South = East  The shortest distance = 15 km  A's left hand will point east. PV PUBLICATION BRING YOU SUCCESS  DIRECTION AND DISTANCE 36. 42. Subhash Nagar (x)m. B C A Ambedkar Nagar Gandhi Nagar (x) m. (x) m. (x) m. Bharat Nagar AC = x+x = (2x) m. The direction of Bharat Nagar from Subhash Nagar AB = (x) m. (  ) = South  AC is 2 times of AB. 37. House 43. Initial Direction: (North) A Right Left 50m 30m Left 20m A left turn from North = West The direction of her house from A (  ) = North-West 44. The actual position of both hands at 12:30 Hour-hand : North 38. 5feet B D A Minute-hand : South Now, hour-hand: North + 90° clockwise = East 6feet 6feet At 2:45 the actual position of hour-hand = East C  Hour hand will point  East +90° clockwise = South 4feet E 45. At 4:30, the actual position of both hands: Starting point = A Hour-hand : South-East Ending point = D Minute-hand : South BD = CE = 4 feet Now minute hand  South+90° Anticlockwise = East NOTE: We considered East, initial direction.  Hour-hand  South-East +90° anticlockwise = 39. 40m North-East 46.  South-East+135° Anticlockwise = North  West + 135° anticlockwise = South - East 30m 30m 47.  South-East + 45° anticlockwise = East  North-East + 45° anticlockwise = North North-East will be called North. 50m A B 48. T S Starting point = A Ending point = B  AB = 50-40 = 10 m P Q 40. Raju’s House 300m R Sam’s House The direction of R from S (  ) = South-West 300m 49. Since Right of East (Q) = South Balu’s House  T travelled in South and  The position of Sam's House in relation to Raju's S travelled in (opposite of South) = North (  ) = South-West Hence M & S travelled in same direction. 41. The actual position of hour hand at 6:00 = South 50. D M While it points to North in the question South + 180° clockwise = North Now at 9:15 the actual position of minute-hand = East  The minute-hand will point = East + 180° clock- K F wise = West The direction of M from K (  ) = North-East PV PUBLICATION BRING YOU SUCCESS