There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?
Answer & explanation
Answer: (c) 31 km
Plotting the places on a grid shows two road routes from D to F: via C, A and B (6 + 10 + 6 + 9 km) and via E and G (5 + 14 + 12 km). Both total 31 km.
- Put A at (0, 0), with east = +x and north = +y.
- B = (0, 6); C = (10, 0); D = 6 km south of C = (10, −6); E = 5 km west of D = (5, −6); F = 9 km west of B = (−9, 6); G = 12 km south of F = (−9, −6).
- Route D → C → A → B → F: 6 + 10 + 6 + 9 = 31 km.
- Route D → E → G → F: 5 + 14 + 12 = 31 km (E to G runs from x = 5 to x = −9).
- Either way the distance is 31 km.
Remember · For direction-and-road items, fix one place as the origin and write coordinates; route lengths then follow by simple addition.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·