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 ?

(a) 20 km
(b) 25 km
(c) 31 km ✓ UPSC's answer
(d) 37 km

Why the answer is (c)

• Set up a coordinate system with A at (0, 0). Since A is 6 km south of B, B is at (0, 6). Since A is 10 km west of C, C is at (10, 0). Since C is 6 km north of D, D is at (10, -6). Since D is 5 km east of E, E is at (5, -6). Since F is 9 km west of B, F is at (-9, 6). Since F is 12 km north of G, G is at (-9, -6). The available roads are AB, AC, CD, DE, BF, EG, and FG. The person travels from D to F. The only path connecting D to F using the given roads is D -> C -> A -> B -> F. The distance D to C is 6 km (vertical). The distance C to A is 10 km (horizontal). The distance A to B is 6 km (vertical). The distance B to F is 9 km (horizontal). The total distance is 6 + 10 + 6 + 9 = 31 km.

Why the other options are wrong

(a) 20 km: 20 km is incorrect because it likely sums only a subset of the required segments or miscalculates the path length.
(b) 25 km: 25 km is incorrect because it does not account for the full distance of the D-C-A-B-F route.
(d) 37 km: 37 km is incorrect because it overestimates the distance, possibly by including unnecessary detours or miscalculating segment lengths.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.