‘A’ started from his house and walked 20 m towards East, where his friend ‘B’ joined him. They together walked 10 m in the same direction. Then ‘A’ turned left while ‘B’ turned right and travelled 2 m and 8 m respectively. Again ‘B’ turned left to travel 4 m followed by 5 m to his right to reach his office. ‘A’ turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices?
Answer & explanation
Answer: (b) 17 m
Plotting the walks from A's house, A's office is at (42, 2) and B's at (34, −13). They are 8 m apart east–west and 15 m apart north–south, so the straight-line distance is 17 m.
- Take A's house as (0, 0), East as +x and North as +y.
- 20 m + 10 m East: both reach (30, 0).
- A turns left (North) 2 m → (30, 2), then right (East) 12 m → A's office at (42, 2).
- B turns right (South) 8 m → (30, −8), left (East) 4 m → (34, −8), right (South) 5 m → B's office at (34, −13).
- Separation: 42 − 34 = 8 m East–West and 2 − (−13) = 15 m North–South.
- Distance = √(8² + 15²) = √289 = 17 m.
Remember · Use coordinates for direction puzzles; left and right depend on the direction currently faced.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·