Question

A person \(M\) starts walking from a point \(P\) straight towards East. After walking \(100\) feet, he turns to left and walks \(45\) feet straight. He again turns left and walks a distance of \(60\) feet straight. Then he turns to the left and walks a distance of \(45\) feet. The distance between \(M\) and \(P\) in feet, is

• A. \(60\)
• B. \(55\)
• C. \(45\)
• D. \(40\)

Hint:

In direction questions, draw the path or track coordinates step by step. Opposite movements cancel each other.

Answer 1

The Correct Option is D

Concept:
This is a direction and distance problem. We track the movement step by step using East-West and North-South directions.

Step 1: Start from point \(P\).
Let the starting point \(P\) be: \[ (0,0) \] The person first walks \(100\) feet towards East. So, his new position becomes: \[ (100,0) \]

Step 2: First left turn.
When a person is facing East and turns left, he faces North. He walks \(45\) feet North. So, the new position becomes: \[ (100,45) \]

Step 3: Second left turn.
Now he is facing North. If he turns left, he faces West. He walks \(60\) feet West. So, the \(x\)-coordinate decreases by \(60\): \[ 100-60=40 \] Hence, the new position becomes: \[ (40,45) \]

Step 4: Third left turn.
Now he is facing West. If he turns left, he faces South. He walks \(45\) feet South. So, the \(y\)-coordinate decreases by \(45\): \[ 45-45=0 \] Hence, the final position of \(M\) is: \[ (40,0) \]

Step 5: Find distance between \(M\) and \(P\).
Starting point: \[ P=(0,0) \] Final point: \[ M=(40,0) \] Distance between \(P\) and \(M\) is: \[ PM=\sqrt{(40-0)^2+(0-0)^2} \] \[ PM=\sqrt{40^2} \] \[ PM=40 \]

Step 6: Final answer.
Therefore, the distance between \(M\) and \(P\) is: \[ 40\ \text{feet} \] \[ \therefore \text{Correct Answer is (D)} \]