Explanation:

- Sameera starts at her house and walks some distance east.

- She then turns right (south) and walks 100 meters.

- She takes a left turn (east) and walks another 30 meters.

- Finally, she takes a left turn again (north) and walks 40 meters to reach the market.

- The air distance (straight line) from her house to the market is 100 meters.

To find out how far she initially walked east:

- Since she ends up north from her original east-west line, we can create a right triangle.

- The northward distance cancels out, which simplifies calculations.

For horizontal distance:

- Total eastward distance: initial unknown distance + 30 meters.

- Calculate hypotenuse using the right triangle formula: \( a^2 + b^2 = c^2 \).

- \( 100^2 = (40 + 30 + x)^2 + 0^2 = 100^2 \).

Finding \( x \):

- Solve: \( 100^2 = (70 + x)^2 \).

Thus, the correct initial distance east would be:

- 50 m $$ \text{(Because } 60 + 40 = 100 \text{ and } 80 + 20 = 100)$$

- Correct Answer: 50 m