GATE ME 2022 Set 1 — Question 42

MCQ+2 / -0.67MediumPERT & CPMOperations ResearchIndustrial Engineering

Industrial Engineering → Operations Research → PERT & CPM

Last updated 5 September 2026

Question

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

Correct answer (B) 10 Solution 1. Forward Pass (Earliest Start/Finish): A: ES=0, EF=2 B: ES=0, EF=3 C: ES=0, EF=2 D: ES=2, EF=6 E: ES=3, EF=8 F: ES=3, EF=7 G: ES=2, EF=5 H: ES=max(6, 8)=8, EF=18 I: ES=7, EF=12 J: ES=5, EF=13 K: ES=max(18, 12, 13)=18, EF=21 Project Duration = 21 hours. 2. Backward Pass (Latest Start/Finish): K: LF=21, LS=18 H: LF=18, LS=8 I: LF=18, LS=13 J: LF=18, LS=10 G: LF=LS of J = 10. The latest finish time for activity G is 10 hours. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) 10 Solution 1. Forward Pass (Earliest Start/Finish): A: ES=0, EF=2 B: ES=0, EF=3 C: ES=0, EF=2 D: ES=2, EF=6 E: ES=3, EF=8 F: ES=3, EF=7 G: ES=2, EF=5 H: ES=max(6, 8)=8, EF=18 I: ES=7, EF=12 J: ES=5, EF=13 K: ES=max(18, 12, 13)=18, EF=21 Project Duration = 21 hours. 2. Backward Pass (Latest Start/Finish): K: LF=21, LS=18 H: LF=18, LS=8 I: LF=18, LS=13 J: LF=18, LS=10 G: LF=LS of J = 10. The latest finish time for activity G is 10 hours.

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