Reasoning: Direction Sense Set 3

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