Amar drives 20 km towards the East from his home to reach a hospital.\nFrom the hospital, he turns left and travels 30 km, and then again turns left and travels 20 km to reach his school.\nHow far is his school from his home (the starting point)?

Introduction / Context:
Originally framed in terms of the distance from the hospital, this question is best interpreted as a standard direction sense and distance problem comparing Amar's school and home. Amar travels in a rectangular path with two left turns, and we must determine the straight-line distance between his home and his final destination, the school. This is a classic application of coordinate tracking and the Pythagoras theorem in a real-life driving scenario.

Given Data / Assumptions:

• Amar starts from his home.
• He drives 20 km towards the East to reach the hospital.
• From the hospital, he turns left and drives 30 km, which means he goes towards the North.
• Then he again turns left and drives 20 km to reach his school, which takes him towards the West.
• We are asked for the straight-line distance between his school and his home.
• All turns are 90 degree left turns and roads are straight.
• We use the standard direction convention: from East, left is North; from North, left is West.

Concept / Approach:
We track Amar's movements on a coordinate plane, representing home as the origin. After his route, the school's coordinates can be calculated. Once we have the coordinates of both home and school, the distance between them is simply the length of the straight line joining these points. Given that Amar's path forms the sides of a right-angled triangle (one leg vertical and one leg horizontal), the Pythagoras theorem can be used to find the distance: distance^2 = (horizontal difference)^2 + (vertical difference)^2.

Step-by-Step Solution:
Step 1: Place Amar's home at (0, 0). Step 2: He drives 20 km East to the hospital, reaching (20, 0). Step 3: From facing East, a left turn is towards North. He drives 30 km North to reach (20, 30). Step 4: From facing North, another left turn means he now faces West. Driving 20 km West takes him to (0, 30), which is the location of his school. Step 5: Home is at (0, 0) and the school is at (0, 30). The horizontal difference is 0, and the vertical difference is 30 km. Step 6: Therefore, the straight-line distance between his home and his school is simply 30 km.

Verification / Alternative check:
We can visualize his journey as forming a rectangle: one side is 20 km East–West, and the other side is 30 km North–South. However, because the last 20 km West leg exactly cancels the first 20 km East leg in terms of horizontal position, the school ends up directly North of the home. That means the shortest distance between home and school is just the vertical side of 30 km, not the diagonal. This matches the coordinate calculation, confirming that the required distance is 30 km.

Why Other Options Are Wrong:
25 km and 27 km are typical distractors that might arise from guessing or misapplying Pythagoras to incorrect legs of a triangle, but they do not match the actual geometry. 35 km is too large and would require an additional, uncompensated displacement. 20 km would only be correct if the school lay directly East or West of home at the same North–South level, which is not the case here, since the school is 30 km North of home after the journey.

Common Pitfalls:
Candidates sometimes mistakenly compute the distance between the hospital and the school, or misread the question, instead of focusing on home-to-school distance. Another mistake is to add all the distances (20 + 30 + 20) or to use Pythagoras on non-perpendicular legs, leading to incorrect answers. Carefully plotting the points and noting that the first and last legs cancel horizontally are key steps for avoiding these errors.

Final Answer:
Amar's school is 30 km away from his home in a straight line.