Raghav left his home for office in a car. He drove 15 km straight towards…
2017
Raghav left his home for office in a car. He drove 15 km straight towards North and then turned eastwards and covered 8 km. He then turned to the left and covered 1 km. He again turned left and drove for 20 km and reached the office. How far and in which direction is his office from his home?
Answer: A. 20 km North-West — Concept. In a direction-sense problem, fix a compass grid (North = up, East = right) and treat the traveller as a moving point. Each left or right turn…
- A.
20 km North-West
- B.
15 km North-West
- C.
30 km North-West
- D.
25 km North
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept. In a direction-sense problem, fix a compass grid (North = up, East = right) and treat the traveller as a moving point. Each left or right turn rotates the facing direction by 90°. After the whole path is plotted, the straight-line distance from start to end is the hypotenuse of the net East–West and net North–South offsets: distance = √(a2 + b2), and the final compass direction is read from the signs of those two offsets.
Tracing the route:
Start at home and drive 15 km North → the car is 15 km North of home, facing North.
Turn to face East and drive 8 km → now 8 km East and 15 km North of home, facing East.
Facing East, a left turn points North; drive 1 km → now 8 km East and 16 km North of home, facing North.
Facing North, a left turn points West; drive 20 km → the 20 km West cancels the 8 km East and leaves 12 km West, so the office is 12 km West and 16 km North of home.
Cross-check. Net displacement: 12 km West and 16 km North. So distance = √(122 + 162) = √(144 + 256) = √400 = 20 km. The office lies both North and West of home, i.e. the North-West direction. Hence the office is 20 km North-West of home.