Q1. A man is facing west. He turns 45º in the clockwise direction and then another 180º in the same direction and then 270º in the anti-clockwise direction. Which direction is he facing now? [RRB, 2005]
The man initially faces in the direction in the West. On moving 45º clockwise, he faces in the North-west direction. On further moving 180° clockwise, he faces in the direction South-east. Finally, on moving 270° anti-clockwise, he faces in the South-west direction.
Q2. If you are facing north-east and move 10 m forward, turn left and move 7.5 m, then you are [MBA, 2002]
a. North of your initial position
b. South of your initial position
c. East of your initial position
d. 12m from your initial position
e. Both (c) and (d)
The narrator starts from a point, moves towards north-east a distance of 10 m, turns left (90° anti-clockwise) and moves 7.5 m upto C.
Clearly, C lies to the north of A. Also triangle ABC is right-angled at B.
AC2 = AB2 + BC2 = (10)2 + (7.5)2
= 100 + 56.25
So, AC = √156.25 m = 12.5 m
Thus, the narrator is 12.5 m to the north of his initial position
Q3. One day, Ravi left home and cycled 10 km southwards, turned right and cycled 5 km and turned right and cycled 10 km and turned left and cycled 10 km. How many kilometers will he have to cycle to reach his home straight?
a. 10 km
b. 15 km
c. 20 km
d. 25 km
Ravi starts from home at A, moves 10 km southwards upto B, turns right and moves 5 km upto C, turns right again and moves 10 km upto D and finally turns left and moves 10 km upto E. Thus, his distance from initial position A
= AE = AD + DE = BC + DE = (5 + 10) km = 15 km
Q4. A child is looking for his father. He went 90 metres in the east before turning to his right. He went 20 metres before turning to his right again to look for his father at his uncle’s place 30 metres from this point. His father was not there. From there, he went 100 metres to his north before meeting his father in a street. How far did the son meet his father from the starting point?
a. 80 metres
b. 100 metres
c. 140 metres
d. 260 metres
The child moves from A, 90 m eastwards upto B, then turns right and moves 20 m upto C, then turns right and moves 30.m upto D. Finally, he turns right and moves 100 m upto E.
AB = 90 m, BF = CD = 30 m.
AF = AB – BF = 60 m.
DE = 100 m, DF = BC = 20 m.
EF = DE – DF = 80 m.
The distance from starting point A = AE = √(AF)^2 + (EF)^2
= √(60)^2 + (80)^2
= 100 m
Q4.. Kailash faces towards north. Turning to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his right. He then turns to his right again and walks 55 metres. Finally, he turns to the right and moves 40 metres. In which direction is he now from his starting point? [MBA, 2006]
Kailash turns right towards right from north direction. So, he walks 25 m towards east upto B, turns left and moves 30 m upto C, turns right and goes 25 m upto D. At D, he turns to right towards the south and walks 55 m upto E. Next, he again turns to right and walks 40 m upto F, which is his final position. F is to the South-east from his starting point
Q6. Deepa moved a distance of 75 metres towards the north. She then turned to the left and walking for about 25 metres, turned left again and walked 80 metres. Finally, she turned to the right at an angle of 45°. In which direcrion was she moving finally?
Deepa started from A. moved 75 m upto B, turned left and walked 25 m upto C. She then turned left again and moved 80 m upto D. Turning to the right at an angle of 45°, she was finally moving in the direction DE i.e. South-west
Q7. 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 tp his starting point? [MBA, 1998]
a. 5 km West
b. 7 km West
c. 7 km East
d. 5 km North-east
Kunal moves from A 10 km towards North upto B, then moves 6 km south upto C, turns towards East and walks 3 km upto D.
Thus, AC = (AB – BC) = (10 – 6) = 4 km
CD = 3 km
So, Kunal’s distance from starting point A
= AD = √(AC)^2 + (CD)^2
= √(4)^2 + (3)^2
= 5 km
D is to the North-east of A
Q8. Johnson left for his office in his car. He drove 15 km towards north and then 10 km towards west. He then turned to the south and covered 5 km. Further, he turned to the east and moved 8 km. Finally, he turned right and drove 10 km. How far and in which direction is he from his starting point? [MBA, 2006]
a. 2 km West
b. 5 km East
c. 6 km South
d. None of these
Johnson drove 15 km from A to B northwards and then 10 km from B to C towards west. He then moves 5 km southwards from C to D and 8 km eastwards upto E. Finally, he turned right and moved 10 km upto F.
A and F lie in the same straight line and F lies to the west of A.
So, Johnson’s distance from the starting point A = AF = (BC – DE) = (10 – 8) km = 2 km