Question

Rakesh left home and walked 5km southwards, then turned right and walked 2km and again turned right and walked 5 km and finally again turned left and walked 5 km. The shortest distance between the final position and home is.

• A. 6 km
• B. 7 km
• C. 9 km
• D. 10 km

Hint:

Using a simple coordinate system (x,y) is one of the most reliable ways to solve path-tracing problems, especially for finding the shortest distance. North/South movement affects the y-coordinate, and East/West affects the x-coordinate.

Answer 1

The Correct Option is B

Step 1: Trace Rakesh's path and track the net displacement in North-South and East-West directions.
Let the starting point (home) be the origin.
- Walked 5km South: Net displacement = -5 km (South).
- Turned right (from South is West) and walked 2km: Net displacement = -5 km (South), -2 km (West).
- Turned right (from West is North) and walked 5km: Net displacement = (-5+5) km (South/North) = 0 km. Net West displacement remains -2 km.
- Turned left (from North is West) and walked 5km: Net N-S displacement is 0. Net West displacement = (-2-5) = -7 km.
Step 2: Calculate the final position and shortest distance.
The final position is 7 km West of the starting point.
The shortest distance is the straight-line distance, which is 7 km.