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)
• Place A at (0, 0) with east as +x and north as +y. Then B = (0, 6), C = (10, 0), D = (10, −6), E = (5, −6), F = (−9, 6) and G = (−9, −6).
• Route 1, D → C → A → B → F: 6 + 10 + 6 + 9 = 31 km.
• Route 2, D → E → G → F: 5 + 14 + 12 = 31 km (E to G is 5 − (−9) = 14 km).
• Both routes along the given roads cover 31 km, so the distance is 31 km, option (c).
Why the other options are wrong
- (a) 20 km
- 20 km is shorter than either route along the given roads; both D–C–A–B–F and D–E–G–F measure 31 km.
- (b) 25 km
- 25 km does not match either route along the given roads; both measure 31 km.
- (d) 37 km
- 37 km is longer than either route along the given roads; both measure 31 km.
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.