A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km, She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house?

The correct option is 25 km.

To find the shortest distance between the bank employee's house and her bank, let us track her movements step-by-step on a 2D Cartesian coordinate system starting from her house at the origin (0, 0):

1. Initial position (House):
Starting Point: (0, 0)

2. First movement: Drives 10 km towards South.
New position: (0, -10)

3. Second movement: Turns left (facing East) and drives 20 km.
New position: (0 + 20, -10) = (20, -10)

4. Third movement: Turns left again (facing North) and drives 40 km.
New position: (20, -10 + 40) = (20, 30)

5. Fourth movement: Turns right (facing East) and drives 5 km.
New position: (20 + 5, 30) = (25, 30)

6. Fifth movement: Turns right again (facing South) and drives 30 km to reach her bank.
Final position (Bank): (25, 30 - 30) = (25, 0)

Now, let us calculate the total net displacement along the horizontal (East-West) and vertical (North-South) directions from the house (0, 0) to the bank (25, 0):

Net horizontal displacement (East) = 25 km

Net vertical displacement (North) = 0 km

Using the distance formula to find the shortest (straight-line) distance between her house (0, 0) and the bank (25, 0):

$\text{Distance}=\sqrt{{(25-0)}^2+{(0-0)}^2}$

$\text{Distance}=\sqrt{{25}^2}=25\text{km}$

Therefore, the shortest distance between her bank and her house is 25 km.