Anil after travelling 6 km towards East from his house realized that he has travelled in a wrong direction. He turned and travelled 12 km towards West, turned right and travelled 8 km to reach his office. The straight distance of the office from his house is:
10 km
Direction problems are solved by tracking net displacement along the two axes rather than by adding up the distances walked.
Take the house as the origin, East as positive along the horizontal axis and North as positive along the vertical axis.
Anil first travels 6 km East, putting him at 6 km East of the house. He then travels 12 km West. Since 12 km West cancels the 6 km East and carries him 6 km beyond, he is now 6 km West of the house.
At that point he turns right. He is facing West, so his right hand points North. Travelling 8 km takes him 8 km North.
The office is therefore 6 km West and 8 km North of the house. These two displacements are perpendicular, so the straight distance is the hypotenuse of a right triangle with legs 6 and 8. By Pythagoras the distance is the square root of 36 + 64, that is the square root of 100, which is 10 km. This is the familiar 6-8-10 triangle, a scaled 3-4-5.
The distractor 20 km is the sum 6 + 12 + 8 minus nothing meaningful, and 14 km is 6 + 8 added directly without recognising that the legs are perpendicular. The commonest slip is turning South instead of North by forgetting that he is facing West when he turns right, though by symmetry that would still give 10 km.
Hence the straight distance of the office from the house is 10 km.
Similar Questions
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
