Step-by-Step Path Analysis

Let's track Raghav's position on a coordinate grid, with his home at the origin (0, 0). We'll use the x-axis for East-West movement and the y-axis for North-South movement.

1. 
   Drives 15 km North: His new position is (0, 15).
   


2. 
   Turns East and drives 8 km: His new position is (0 + 8, 15), which is (8, 15).
   


3. 
   Turns left (now facing North) and drives 1 km: His new position is (8, 15 + 1), which is (8, 16).
   


4. 
   Turns left (now facing West) and drives 20 km: His final position is (8 - 20, 16), which is (-12, 16). This is the office.
   

Final Distance and Direction from Home

• 
  Final Position: The office is at (-12, 16) relative to the home at (0, 0). This means the office is 12 km West and 16 km North of the home.
  


• 
  Direction: Since the final position is North and West of the starting point, the overall direction is North-West.
  


• 
  Distance (Pythagorean Theorem): The shortest distance is the hypotenuse of a right-angled triangle with sides 12 km and 16 km.
  
  Distance² = (12)² + (16)²

Distance² = 144 + 256 = 400

Distance = √400 = 20 km
  

Final Answer: The office is 20 km North-West from the home.