# Q. 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?

(a) 20 km

(b) 25 km

(c) 30 km

(d) 35 km

Correct Answer: (b) 25 km

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation : **

## Finding Shortest Distance Between Bank & House

The correct answer is indeed (b) 25 km.

To understand why this is the case, let’s visualize the employee’s journey on a coordinate plane. Let’s assume that her house is located at the origin (0,0). She first drives 10 km towards South from her house. This means she moves 10 units in the negative y-direction and her new position is (0,-10).

She then turns to her left and drives another 20 km. Since she was facing South and turned left, she is now facing East. So she moves 20 units in the positive x-direction and her new position becomes (20,-10).

She again turns left and drives 40 km. Since she was facing East and turned left, she is now facing North. So she moves 40 units in the positive y-direction and her new position becomes (20,30).

Then she turns to her right and drives for another 5 km. Since she was facing North and turned right, she is now facing East. So she moves 5 units in the positive x-direction and her new position becomes (25,30).

She again turns to her right and drives another 30 km to reach her bank where she works. Since she was facing East and turned right, she is now facing South. So she moves 30 units in the negative y-direction and finally reaches her bank at position (25,0).

The shortest distance between two points on a coordinate plane can be calculated using the Pythagorean theorem: distance = sqrt((x2-x1)^2 + (y2-y1)^2). In this case, we want to find the shortest distance between her house at (0,0) and her bank at (25,0).

Plugging these values into our formula gives us: distance = sqrt((25-0)^2 + (0-0)^2) = sqrt(625) = 25.