A man travels 7 km towards East, he turns left and travels 8 km, again he turns left and travels 10 km. Finally, he turns left and travels 2 km. In which direction is he from his starting point?

Options

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

Answer

To solve the problem step by step, let's break down the man's journey:

1. **Starting Point**: Let's denote the starting point as point A.

2. **First Movement**: The man travels 7 km towards the East.
- From point A, he moves to point B (7 km East).

3. **Second Movement**: He turns left and travels 8 km.
- Since he was facing East, turning left means he is now facing North. He moves from point B to point C (8 km North).

4. **Third Movement**: He turns left again and travels 10 km.
- Now facing North, turning left means he is facing West. He moves from point C to point D (10 km West).

5. **Fourth Movement**: Finally, he turns left and travels 2 km.
- Facing West, turning left means he is now facing South. He moves from point D to point E (2 km South).

Now, let's summarize the movements:

- From A to B: 7 km East
- From B to C: 8 km North
- From C to D: 10 km West
- From D to E: 2 km South

Now, let's calculate the final position relative to the starting point A:

- **Final Position**:
- East-West Movement:
- He moved 7 km East and then 10 km West.
- Net movement = 10 km West - 7 km East = 3 km West.

- North-South Movement:
- He moved 8 km North and then 2 km South.
- Net movement = 8 km North - 2 km South = 6 km North.

Now, we can determine the final position E relative to A:

- The man is now 3 km to the West and 6 km to the North of the starting point A.

**Conclusion**: To find the direction from the starting point A to the final point E, we can visualize this on a coordinate plane. The final position is in the North-West direction from the starting point.

Thus, the man is in the **North-West** direction from his starting point.