Question

The project activities are given in the following table along with the duration and dependency. \[ \begin{array}{|c|c|c|} \hline \text{Activities} & \text{Duration (days)} & \text{Depends on} \\ \hline P & 10 & - \\ Q & 12 & - \\ R & 5 & P \\ S & 10 & Q \\ T & 10 & P, Q \\ \hline \end{array} \] Which one of the following combinations is correct?

• A. Total duration of the project = 22 days, Critical path is Q → S
• B. Total duration of the project = 20 days, Critical path is Q → T
• C. Total duration of the project = 22 days, Critical path is P → T
• D. Total duration of the project = 20 days, Critical path is P → R

Hint:

The critical path is the longest path in a project schedule and determines the shortest possible project duration.

Answer 1

The Correct Option is A

The critical path method (CPM) is used to determine the longest path through the project network and the total time required for project completion. - The project activities are as follows:
- P: 10 days
- Q: 12 days
- R: 5 days (depends on P)
- S: 10 days (depends on Q)
- T: 10 days (depends on P and Q)
To calculate the total duration, we need to find the longest path through the network: - Path 1: P → R = 10 + 5 = 15 days
- Path 2: Q → S = 12 + 10 = 22 days
- Path 3: P → T = 10 + 10 = 20 days
- Path 4: Q → T = 12 + 10 = 22 days
Thus, the longest path is Q → S, with a total duration of 22 days.

Final Answer: (A) Total duration of the project = 22 days, Critical path is Q → S.