Question

Starting from a Point 'M' Harish walked \(18\) m towards South. He turned to his left and walked \(5\)m. He then turned to his left and walked \(18\) m. He again turned to his left and walked \(35\) m and reached a point 'P'. How far is Harish from the point 'M' and in which direction?

• A. \(10\) m East
• B. \(10\) m South
• C. \(10\) m West
• D. None of these

Hint:

For direction questions, convert every movement into coordinates. This avoids confusion in left and right turns.

Answer 1

The Correct Option is D

Concept:
This is a direction sense problem. The easiest method is to take the starting point as the origin and track movement using coordinates. Let: \[ \text{East} = +x \] \[ \text{West} = -x \] \[ \text{North} = +y \] \[ \text{South} = -y \]

Step 1: Start from point \(M\).
Let: \[ M=(0,0) \] Harish first walks \(18\) m towards South. So his position becomes: \[ (0,-18) \]

Step 2: Turn left from South.
When a person faces South, his left direction is East. He walks \(5\) m East. So: \[ (0,-18)\rightarrow(5,-18) \]

Step 3: Turn left from East.
When a person faces East, his left direction is North. He walks \(18\) m North. So: \[ (5,-18)\rightarrow(5,0) \]

Step 4: Turn left from North.
When a person faces North, his left direction is West. He walks \(35\) m West. So: \[ (5,0)\rightarrow(5-35,0) \] \[ =(-30,0) \]

Step 5: Find distance and direction from \(M\).
Final position is: \[ P=(-30,0) \] Starting point was: \[ M=(0,0) \] So Harish is \(30\) m to the West of \(M\).

Step 6: Check the options.
Option (A) \(10\) m East is incorrect.
Option (B) \(10\) m South is incorrect.
Option (C) \(10\) m West is incorrect because the distance is \(30\) m West.
Option (D) None of these is correct. Hence, the correct answer is: \[ \boxed{(D)\ \text{None of these}} \]