Question

In a project network, two parallel activities start from the same node and merge at the same succeeding node. Their durations are: Activity A = 6 days, Activity B = 9 days. Which statement is correct?

• A. Both activities lie on the critical path
• B. Only Activity A lies on the critical path
• C. Only Activity B lies on the critical path
• D. Neither activity lies on the critical path

Hint:

For parallel activities sharing the same start and end nodes, the activity with the maximum duration acts as the bottleneck and will always lie on the critical path.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks us to identify which of the two parallel activities starting and ending at the same nodes belongs to the critical path, given their respective completion times.

Step 2: Key Formula or Approach:
The critical path in a project network is defined as the path with the longest duration from start to finish.
The activities lying on this path have zero total float (slack), meaning any delay in these activities directly delays the entire project completion time.

Step 3: Detailed Explanation:

• Let the start node be Node 1 and the merge node be Node 2.

• Activity A (6 days) and Activity B (9 days) both start at Node 1 and end at Node 2 in parallel.

• The earliest time that the project can proceed past Node 2 is determined by the longer of the two activities, which is Activity B.

• Specifically, the minimum time to transition from Node 1 to Node 2 is 9 days.

• Activity B determines this duration and therefore has zero float; thus, it is a critical activity.

• Activity A, taking only 6 days, can be delayed by up to \(9 - 6 = 3\) days without affecting the overall project duration. It has a total float of 3 days and is non-critical.

Step 4: Final Answer:
Consequently, only Activity B lies on the critical path.