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?

The correct option is 31 km.

To find the total distance covered by the person traveling from place D to place F through the specified roads, let us first trace the route connecting D and F using the given information about the positions and road lengths between the places.

Step 1: Understand the given connections and distances

• Road AB: A is 6 km south of B (Distance AB = 6 km)
• Road AC: A is 10 km west of C (Distance AC = 10 km)
• Road CD: C is 6 km north of D (Distance CD = 6 km)
• Road DE: D is 5 km east of E (Distance DE = 5 km)
• Road BF: F is 9 km west of B (Distance BF = 9 km)
• Road EG: Not directly on the shortest connecting path between D and F
• Road FG: F is 12 km north of G (Distance FG = 12 km)

Step 2: Identify the path from D to F

We need to find the route that connects place D to place F using the available roads:

1. From D, we can travel along road CD to reach C.
2. From C, we travel along road AC to reach A.
3. From A, we travel along road AB to reach B.
4. From B, we travel along road BF to reach F.

Thus, the complete path from D to F through these roads is: D ⇒ C ⇒ A ⇒ B ⇒ F.

Step 3: Calculate the total distance covered

The total distance covered along this path is the sum of the individual road distances:

$\text{Total Distance}=\text{Distance(DC)}+\text{Distance(CA)}+\text{Distance(AB)}+\text{Distance(BF)}$

Substituting the given values into the equation:

$\text{Total Distance}=6\text{km}+10\text{km}+6\text{km}+9\text{km}$

$\text{Total Distance}=31\text{km}$

Therefore, the total distance covered by the person traveling from D to F is 31 km.