Question : Direction: A man travels 4 kilometres due north, then travels 6 kilometres due east, and further travels 4 kilometres due north. How far is he from the starting point?
Option 1: 8 km
Option 2: 10 km
Option 3: 6 km
Option 4: 14 km
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Correct Answer: 10 km
Solution : As per the given information, the movement of the man looks as follows –
The direct distance between his starting point and the endpoint is AD as shown below –
Produce DC to O and join AO to form a right-angled triangle at O, with AD as hypotenuse, AO as base, and DO as perpendicular.
According to the rectangular properties, i.e., opposite sides are equal, so, AO = 6 km, CO = 4 km ⇒ DO = 8 km.
In right-angled triangle AOD, use Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
(AD)2 = (DO)2 + (AO)2
(AD)2 = 82 + 62
(AD)2 = 64 + 36 ⇒ (AD)2 = 100 ⇒ AD = (100)½
AD = 10
Distance between his starting point and the endpoint = 10 km.
Hence, the second option is correct.
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Question : Directions: Pranav went 10 kilometres to the north. Then he turned West and covered 10 kilometres. Then he turned south and covered 5 kilometres. Finally, he turned to the east and covered 10 kilometres. In which direction is he from the starting point?
Option 1: South
Option 2: North
Option 3: East
Option 4: West
Question : Directions: Johnson left for his office in his car. He drove 15 km towards the North and then 10 km towards the West. He then turned to the South and covered 5 km. Further, he turned to East and moved 8 km. Finally, he turned right and moved 10 km. How far and in which direction is he from his starting point?
Option 1: 2 km, West
Option 2: 5 km, East
Option 3: 3 km, North
Option 4: 3 km, South
Question : Directions: Rajesh walks 2 km to the south, then turns northeast and walks 3 km. Then he turns south and walks 2 kilometres. Then he turns west and walks 4 kilometres. Finally, he turns northwest and walks 5 kilometres. In which direction is he going from his starting point?
Option 1: North-West
Option 2: North-East
Option 3: South-East
Option 4: South-West
Question : Direction: Naseebah runs for 10 kilometres in the eastern direction. She then turns left and starts walking for 6 kilometres. Again, she turns left and starts running for 6 kilometres. Then she turns left and walks again for 6 km. How far is she from the starting point?
Option 1: 4 km
Option 2: 5 km
Option 4: 3 km
Question : Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?
Option 1: North-East
Option 2: North-West
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