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Reasoning Quiz On Direction & Distance Questions

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1. From a point, Sahil starts walking in east direction. After walking for 15 m he takes a right turn. Now he walks for 12 m before turning to his right again. Next he walks 5 m and again turns in same direction as before. He now walks for 20 m before stopping at a point. How far is this point from the point where Sahil started?
   A) 4 √10 m
   B) 3 √22 m
   C) 7 m
   D) 2√41 m
   E) 12 m
   View Answer

    Option D
   Required distance = √(10² + 8²) = 2√41 m
2. Abhi and Asha start cycle race from point A. They both start in east direction. After cycling for 7 m, Abhi continues straight while Asha takes a left turn. They both cycle for 6 m before turning right and left directions respectively.  Next
   (1) Asha cycles for 8 m and takes a right turn. Now she cycles for 5 m before turning to right again.
   (2) Abhi cycles for 4 m and takes a left turn. Now he cycles for 6m before turning to left again.
   If both stop at these points, how much respective distance they have to travel to meet each other on their current paths?
   A) 10 m, 15 m
   B) 13 m, 17 m
   C) 15 m, 20 m
   D) 18 m, 24 m
   E) Cannot be determined
   View Answer

    Option C
   Solution:
   
3. From point A, Swati started walking in south direction. She walked for 4 m and took a right turn. Next she walked 5 m and turned to her left. Next she walked for 3 m and turned to her right. Next she walked 4 m and turned to her right again. Next she walked 15 m and turned to her right again and stopped at point B after walking 7 m. Find distance AB.
   A) 2√22 m
   B) 3√21 m
   C) 2√19 m
   D) 4√17 m
   E) None of these
   View Answer

   Option E
   Solution:
   
   AB = √(8² +2²) = 2√17 m
4. Point P is 10 m west of point Q. Point R is 4 m north of point P. Point T is 3 m east of point S and point S is 5 m south of point Q. What is the direction of point R with respect to point T?
   A) South-east
   B) South
   C) North-east
   D) North-west
   E) West
   View Answer

   Option D
5. Anaya started from a point in some direction. After walking for some time, she turned to her right and continued walking. Now walking for some distance she turned to her left and after this finally to her right. If now she is walking in west direction, in which direction did she started her journey?
   A) North
   B) West
   C) East
   D) South
   E) East or west
   View Answer

    Option D
   Solution:
   Start from back and direct towards starting direction
   She is walking in west and before that she turned to her right, so she must be travelling in south before turning right.
   Now she was walking in south and before that she turned to her left, so she must be travelling in west before turning left.
   Now she was walking in west and before that she turned to her right, so she must be travelling in south before turning right.
   At last south direction.
6. Sheetal started from point in South direction. After walking for 5 km she took a right turn. Now she walked another 5 km and took a left turn. Then after walking for 2 km she took a right turn. After covering more 2 km she turned 45^o in clockwise direction. She is facing which direction now?
   A) South West
   B) South East
   C) North East
   D) North West
   E) None of these
   View Answer

   Option B
   Solution:
   

Directions (7-8): Point P is 5 m south of point A. Point T is 8 m east of point Q. Point Z is 4 m west of point V. Point P is 6 m west of point B. Point V is 6 m south of point T. Point Q is 4 m south of point B.

7. Find distance AZ.
   A) 5√13 m
   B) 6√13 m
   C) 4√14 m
   D) 7√15 m
   E) 3√11 m
   View Answer

   Option A
   Solution:
   
   Vertical distance = 5+4+6 = 15 m
   Horizontal distance = (PB) + (QT – CV) = 6 + (8-4) = 10 m
   So AZ = √(15² + 10²) = 5√13 m
8. A person starts from point B in north direction. Walks for 6 m and reaches point C, takes a right turn walks for 5 m reaches point F. Again he takes a right turn, walks for 3 m, reaches point H, now takes a left turn, reaches point K, now takes a final right turn to reach point T. Find the area enclosed by points B, Q, T, K, H, F and C.
   A) 58m²
   B) 65m²
   C) 71m²
   D) 76m²
   E) None of these
   View Answer

     Option C
   Solution:
   
   The area will be = Ar. of rectangle QCFD + Ar. of  DHKT = 10*5 + 3*7 = 71m²

Directions (9-10): Point A is 8 m west of point B. Point E is 2 m east of point F. Point G is 3 m east of point H. Point E is 3 m north of point of point D. Point C is 9 m west of point D. Point G is 9 m north of point F. Point C is 6 m south of point B.

9. Find distance AH.
   A) 7√6 m
   B) 7√5 m
   C) 6√6 m
   D) 6√5 m
   E) None of these
   View Answer

     Option D
   Solution:
   
   Vertical distance = GF – (CB – ED) = 9 – (6-3) = 6
   Horizontal distance = AB + (CD – (HG + FE)) = 8 + (9 – (3+2) = 12
   Required distance AH = √(6² + 12²) = 6√5 m
10. A person starts from point G in east direction. Walks for 6 m, takes a right turn, now walks for 5 m. Now he takes a left turn, walks for 3 m, then after two consecutive right turns he reaches point E. Find the distance travelled by him to reach point E.
    A) 27 m
    B) 25 m
    C) 23 m
    D) 24 m
    E) 28 m
    View Answer

    Option B
    Solution:
    
    6 + 5+ 3 + (9-5) + (3+4) = 25 m

Directions (1-5): Study the following information carefully and answer the questions that follow.
A country has the following types of traffic signals.

3 green lights = go at 60 kmph speed
2 green lights = go at 40 kmph speed
1 green light = go at 20 kmph speed
3 red lights = stop
2 red lights = turn left
1 red light = turn right

A person starts driving from a point in West direction and he encounters the following traffic signals:
Starting point – 1 green light;
After 15 minutes, 1st signal – 2 red & 2 green lights;
After 24 minutes, 2nd signal – 1 red & 3 green lights;
After 45 minutes, 3rd signal – 1 red & 2 green lights;
After 18 minutes, 4th signal – 3 red lights;

1. Find the total distance he covered up to the last signal.
   A) 76 km
   B) 78 km
   C) 70 km
   D) 75 km
   E) 79 km
   View Answer

    Option B
   Starting in West direction: 1 green light means 20 km/hr
   So 15 minutes at 20km/hr, means covers 15/60 * 20 = 5 km
   Next, 2 red & 2 green lights, means turn left and 24 minutes at 40 km/hr
   So now distance covered = 24/60 * 40 = 16 km
   Now for next 45 minutes, 1 red & 3 green lights, means turned right and drove at 60 km/hr, so covered 45/60 * 60 = 45 Km
   Next  – 1 red & 2 green lights, turned right and 18 minutes at 40 km/hr
   So covered = 18/60 * 40 = 12 km. Next 3 red lights so stopped
   So total distance = 5+16+45+12 = 78 km
2. After passing the third signal if the person encounters fourth signal after half an hour, then what is his final position with respect to the starting point?
   A) 4 km to the south and 50 km to the east
   B) 55 km directly to the north-west
   C) 4 km to the north and 50 km to the west
   D) 4 km to the north and 45 km to the west
   E) None of these
   View Answer

    Option C
   Solution:
   So at last 1 red & 2 green lights, turned right and 30 minutes at 40 km/hr
   So covered 30/60 * 40 = 20 km
   We get:
   
3. If instead of starting in West direction, the man starts in South direction, then what is his position with respect to the starting point?
   A) 50 km to the south and 4 km to the west
   B) 54 km directly to the north-west
   C) 50 km to the north and 4 km to the west
   D) 50 km to the south and 4 km to the east
   E) None of these
   View Answer

    Option D
   Solution:
   
4. If after the first signal,
   2nd signal: 2 red and 2 green lights, and
   3rd signal: 1 red and 3 green lights, then what is the distance covered up to the last signal?
   A) 69 km
   B) 60 km
   C) 68 km
   D) 67 km
   E) 65 km
   View Answer

    Option A
   Solution:
   Starting in West direction: 1 green light means 20 km/hr
   So 15 minutes at 20km/hr, means covers 15/60 * 20 = 5 km
   Next, 2 red & 2 green lights, means turn left and 24 minutes at 40 km/hr
   So now distance covered = 24/60 * 40 = 16 km
   Now for next 45 minutes, 2 red & 2 green lights, means turned left and drove at 40 km/hr, so covered 45/60 * 40 = 30 Km
   Next  – 1 red & 3 green lights, turned right and 18 minutes at 60 km/hr
   So covered = 18/60 * 60 = 18 km. Next 3 red lights so stopped
   So total distance = 5+16+30+18 = 69 km
5. If the person stops at 3rd signal, then what is his final position with respect to his starting position?
   A) 50 km to the north-west
   B) 52.5 km to the south-west
   C) 52.5 km to the north-east
   D) 50.5 km to the south-west
   E) 50.5 km to the south-east
   View Answer

    Option B
   Solution:
   Starting in West direction: 1 green light means 20 km/hr
   So 15 minutes at 20km/hr, means covers 15/60 * 20 = 5 km
   Next, 2 red & 2 green lights, means turn left and 24 minutes at 40 km/hr
   So now distance covered = 24/60 * 40 = 16 km
   Now for next 45 minutes, 1 red & 3 green lights, means turned right and drove at 60 km/hr, so covered 45/60 * 60 = 45 Km
   Stopped here
   We get:
   

Directions (6-8): Point D is 2 km to the north of point C. Point G is 8 km to the north of point H. Point A is 15 km to the south of point B. Point C is 8 km to the east of point B. Point E is 10 km to the north of point F which is 4 km to the west of point G. Point D is 4 km to the west of point E.

6. Find shortest distance BH.
   A) 16√4 km
   B) 32 km
   C) 15 km
   D) 16√2 km
   E) None of these
   View Answer

    Option D
   Solution:
   
7. If a person after taking 2 turns reaches to point B from point F via point A, then what is the distance that he covered?
   A) 32 km
   B) 34 km
   C) 30 km
   D) 35 km
   E) 36 km
   View Answer

    Option B
   Solution:
   
8. If a person starts from point H and reaches point S which is south of point C, then find distance CS + HS – EF.
   A) 12 km
   B) 13 km
   C) 15 km
   D) 14 km
   E) None of these
   View Answer

     Option D
   Solution:
   Point S is south of point C, so CS = 8+8 = 16 km, HS = 4+4 = 8 km and EF is 10 km
   So required answer = 16 +8 – 10 = 14 km
9. Priya started from point A. after walking for some time, she turned to her right and continued walked, then after some time turned to her right again. Now walking for some distance she turned to her left and after this finally to her right. If now she is walking in west direction, in which direction did she started her journey from point A?
   A) West
   B) East
   C) South
   D) North
   E) Cannot be determined
   View Answer

     Option B
   Solution:
   For this, start from back:
   She is walking in west and before that she turned to her right, so she must be travelling in south before turning right.
   Now she was walking in south and before that she turned to her left, so she must be travelling in west before turning left.
   Now she was walking in west and before that she turned to her right, so she must be travelling in south before turning right.
   Now she was walking in south and before that she turned to her right, so she must be travelling in east before turning right.
   At last east direction.
10. Tiya started from her home to office. She started in east direction. After walking for 4 km she turned to her left and walked 8 km, now she turned left and walked 2 km. After this she turned to right walked 4 km. Now after turning to her right she walked 13 km and reached office. Find the shortest distance between her office and home.
    A) 3√43 m
    B) 3√41 km
    C) 4√41 m
    D) 5√38 m
    E) None of these
    View Answer

      Option B
    Solution:
    √15² + 12² = 3√41 km