I start from my home and go 2 km straight. Then, I turn towards my right and go 1 km. I turn again towards my right and go 1 km again. If I am north-west from my house, then in which direction did I go to in the beginning ?

Options

A. North
B. South
C. East
D. West

Explanation

To solve the problem step by step, we will analyze the movements described in the question and determine the initial direction based on the final position being northwest from the starting point.

### Step-by-Step Solution:

1. **Initial Movement**:
- Start from home and move **2 km straight**.
- Let's assume we start facing **East**.

2. **First Turn**:
- After moving 2 km East, we turn **right**.
- Facing East, turning right means we now face **South**.
- Move **1 km South**.

3. **Second Turn**:
- Now, we turn **right** again.
- Facing South, turning right means we now face **West**.
- Move **1 km West**.

4. **Final Position**:
- After these movements, we need to determine our final position relative to our starting point (home).
- From the starting point (home), we moved:
- 2 km East
- 1 km South
- 1 km West
- The net movement in the East-West direction is:
- 2 km East - 1 km West = 1 km East
- The net movement in the North-South direction is:
- 0 km (since we moved 1 km South and did not move North)
- Therefore, our final position is **1 km East and 1 km South** from home.

5. **Determining the Direction**:
- The final position (1 km East and 1 km South) corresponds to the **South-East** direction from the starting point.
- However, the question states that the final position is **North-West** from home.

6. **Adjusting the Initial Direction**:
- Since we ended up in the South-East direction but need to be in the North-West direction, we need to find out what initial direction would lead to this.
- If we assume we started from the **West** instead of the East, we can repeat the movements:
- Start facing **West**, move 2 km West (now at -2 km East).
- Turn right (now facing North) and move 1 km North (now at -2 km East, +1 km North).
- Turn right again (now facing East) and move 1 km East (now at -1 km East, +1 km North).
- This final position is indeed **North-West** from the starting point.

### Conclusion:
Thus, the initial direction I went in the beginning was **West**.