A man starts from point A, walks 20 km East to reach B, then turns North and walks 15 km to reach C, then turns West and walks 8…

Question

A man starts from point A, walks 20 km East to reach B, then turns North and walks 15 km to reach C, then turns West and walks 8 km to reach D, then turns South and walks 15 km to reach E. What is the distance and direction of point E from point A?

1. A. 3 km East
2. B. 12 km South
3. C. 3 km North
4. D. 12 km East (Correct answer)

Correct Answer

Option D — 12 km East

Detailed Solution & Explanation

The correct answer is 12 km East.

Key Points

• Track the walker's movement on the two axes separately (a direction-sense problem).
• Moves: 20 km East (A→B), 15 km North (B→C), 8 km West (C→D), 15 km South (D→E).
• North–South axis: 15 North − 15 South = 0 (they cancel).
• East–West axis: 20 East − 8 West = 12 km East.
• So point E is 12 km due East of the starting point A.
• resolve every path into net horizontal and net vertical displacement.
• Equal-and-opposite moves on the same axis cancel; here the northward and southward legs (both 15 km) cancel, leaving only the east–west offset.

Exam Tip

• when the vertical (or horizontal) moves cancel exactly, the shortest distance is simply the remaining axis value — no Pythagoras needed.
• Pythagoras is required only when both axes have a leftover component.