A blind person after walking each 10 steps in one direction, each of length 80 cm, turns randomly the left or to right by `90^@`. After walking a total of 40 steps the maximum possible displacement the person from his starting position could be

Options

A. 320 m
B. 32 m
C. 16 m
D. `16sqrt(2) m`

Answer

To solve the problem of the blind person's maximum possible displacement after walking 40 steps, we can break down the solution into clear steps:

### Step-by-Step Solution:

1. **Understanding the Movement**:
- The blind person walks 10 steps in one direction, with each step measuring 80 cm.
- Therefore, after 10 steps, the distance covered is:
\[ \text{Distance} = 10 \times 80 \text{ cm} = 800 \text{ cm} = 8 \text{ m} \]

2. **Total Steps Taken**:
- The person walks a total of 40 steps. Since he walks 10 steps at a time, he will complete:
\[ \text{Total Distance} = 4 \times 8 \text{ m} = 32 \text{ m} \]

3. **Turning Directions**:
- After each set of 10 steps, the person turns either left or right by 90 degrees. This means that the path taken can be visualized as a series of right angles.

4. **Calculating Maximum Displacement**:
- To maximize displacement, the person should ideally walk in a straight line as much as possible. However, due to the turns, we need to analyze the possible paths.
- The maximum displacement occurs when the person makes turns that allow him to move diagonally.

5. **Path Analysis**:
- If the person walks in a square pattern, he can achieve maximum displacement by alternating turns effectively.
- For example, if he walks straight for 8 m, turns right, walks another 8 m, turns left, and continues this pattern, he can reach a point that is diagonally opposite from the starting point.

6. **Using Pythagorean Theorem**:
- The maximum displacement can be calculated using the Pythagorean theorem. If he moves in two perpendicular directions:
\[ \text{Displacement} = \sqrt{(8 \text{ m})^2 + (8 \text{ m})^2} = \sqrt{64 + 64} = \sqrt{128} = 8\sqrt{2} \text{ m} \]

7. **Total Displacement Calculation**:
- Since he can repeat this pattern, the maximum displacement after completing all 40 steps (4 segments of 8 m) can be calculated as:
\[ \text{Maximum Displacement} = 16\sqrt{2} \text{ m} \]

### Final Answer:
The maximum possible displacement of the person from his starting position is:
\[ \boxed{16\sqrt{2} \text{ m}} \]