The correct answer is B) 8 hours. **Step 1: Understand the Constraints and Objective** We need to find the minimum travel time from City P (start) to City T (destination). The key constraints are: 1. The journey must involve **exactly two distinct intermediate cities**. This means the path will be of the form $P \rightarrow X \rightarrow Y \rightarrow T$, where $X$ and $Y$ are intermediate cities chosen from {Q, R, S}, and $X \neq Y$. 2. No city can be visited more than once in a single journey. This implies that P, X, Y, T must all be distinct in the chosen path. **Step 2: List all possible ordered pairs of distinct intermediate cities ($X$, $Y$)** The available intermediate cities are Q, R, S. The possible ordered pairs ($X$, $Y$) are: * (Q, R) * (Q, S) * (R, Q) * (R, S) * (S, Q) * (S, R) **Step 3: Evaluate each possible path $P \rightarrow X \rightarrow Y \rightarrow T$ for validity and total travel time.** We will use the provided travel times, assuming connections are bidirectional. 1. **Path: $P \rightarrow Q \rightarrow R \rightarrow T$** * P-Q: $2$ hours * Q-R: $1$ hour * R-T: $5$ hours * Total time: $2 + 1 + 5 = 8$ hours. * Validity: P, Q, R, T are all distinct. This is a valid path. 2. **Path: $P \rightarrow Q \rightarrow S \rightarrow T$** * P-Q: $2$ hours * Q-S: $4$ hours * S-T: $3$ hours * Total time: $2 + 4 + 3 = 9$ hours. * Validity: P, Q, S, T are all distinct. This is a valid path. 3. **Path: $P \rightarrow R \rightarrow Q \rightarrow T$** * P-R: $3$ hours * R-Q: $1$ hour * Q-T: No direct connection exists between Q and T in the given table. * Validity: This path is invalid. 4. **Path: $P \rightarrow R \rightarrow S \rightarrow T$** * P-R: $3$ hours * R-S: $2$ hours * S-T: $3$ hours * Total time: $3 + 2 + 3 = 8$ hours. * Validity: P, R, S, T are all distinct. This is a valid path. 5. **Path: $P \rightarrow S \rightarrow Q \rightarrow T$** * P-S: No direct connection exists between P and S in the given table. * Validity: This path is invalid. 6. **Path: $P \rightarrow S \rightarrow R \rightarrow T$** * P-S: No direct connection exists between P and S in the given table. * Validity: This path is invalid. **Step 4: Identify the minimum travel time among valid paths** The valid paths and their total travel times are: * $P \rightarrow Q \rightarrow R \rightarrow T$: $8$ hours * $P \rightarrow Q \rightarrow S \rightarrow T$: $9$ hours * $P \rightarrow R \rightarrow S \rightarrow T$: $8$ hours The minimum travel time among these valid paths is $8$ hours. Therefore, the minimum travel time required is $8$ hours.