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?

Path from D to F using the available roads: D → E → G → F. DE = 5 km, EG = ? and GF = 12 km. We need EG. Place coordinates: Let A = (0,0). B is 6 km north of A, so B = (0,6). C is 10 km east of A, so C = (10,0). D is 6 km south of C, so D = (10,-6). E is 5 km west of D, so E = (5,-6). F is 9 km west of B, so F = (-9,6). G is 12 km south of F, so G = (-9,-6). Then EG = |5 - (-9)| = 14 km (E and G are both at y = -6). Total = DE + EG + GF = 5 + 14 + 12 = 31 km. Option (c) is correct.