GATE 2022 ME (ME1) – Question 42
Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.
| Activity | Time (hours) | Immediate predecessors |
|---|---|---|
| A | 2 | − |
| B | 3 | − |
| C | 2 | − |
| D | 4 | A |
| E | 5 | B |
| F | 4 | B |
| G | 3 | C |
| H | 10 | D, E |
| I | 5 | F |
| J | 8 | G |
| K | 3 | H, I, J |
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Show answer and explanation
Correct answer: (B) 10
Explanation
The earliest finish times are: D = 6, E = 8, F = 7, H = $8 + 10 = 18$, I = 12, G = 2, J = 10, and K starts at $\max(18, 12, 10) = 18$ and finishes at 21. So the project time is 21 h. Going backwards, K must start at 18, so J must finish by 18 and start by $18 - 8 = 10$. G precedes only J, so its latest finish time is 10 h.