Question

A person walks \(10\) km towards the north, then turns to his left and walks \(5\) km, and then again turns to his left and walks \(10\) km. How far is he from his starting point now?

• A. \(10\) kilometers
• B. \(20\) kilometers
• C. \(15\) kilometers
• D. \(5\) kilometers

Hint:

In direction problems, always check if movements in opposite directions cancel each other before applying distance formulas.

Answer 1

The Correct Option is D

Concept: Such problems are based on direction sense and displacement. The shortest distance from the starting point to the final position is found using simple geometry or coordinate representation.
Step 1: Trace the path
The person starts from point \(O\).
He walks \(10\) km north to point \(A\).
Turning left, he walks \(5\) km west to point \(B\).
Turning left again, he walks \(10\) km south to point \(C\).
Step 2: Determine the final position The northward and southward movements cancel each other: \[ 10\text{ km north} - 10\text{ km south} = 0 \] So the person is directly west of the starting point by \(5\) km.
Step 3: Find the distance from the starting point \[ \text{Distance} = 5 \text{ km} \]
Final Answer: \(\boxed{5\text{ kilometers}}\)