GATE CE 2021 Set 2 — Question 52

NAT+2 / -0MediumCPMConstruction ManagementStructural EngineeringCritical Path

Structural Engineering → Construction Management → CPM

Last updated 5 September 2026

Question

The activity details for a small project are given in the Table. Activity Duration (days) Depends on A 6 - B 10 A C 14 A D 8 B E 12 C F 8 C G 16 D, E H 8 F, G K 2 B L 5 G, K The total time (in days, in integer) for project completion is________

Correct answer 56 to 56 Solution To find the project completion time, we perform a forward pass to find the Earliest Finish (EF) time for each activity: EF(A) = 6 EF(B) = EF(A) + 10 = 16 EF(C) = EF(A) + 14 = 20 EF(D) = EF(B) + 8 = 24 EF(E) = EF(C) + 12 = 32 EF(F) = EF(C) + 8 = 28 EF(G) = max(EF(D), EF(E)) + 16 = max(24, 32) + 16 = 48 EF(H) = max(EF(F), EF(G)) + 8 = max(28, 48) + 8 = 56 EF(K) = EF(B) + 2 = 18 EF(L) = max(EF(G), EF(K)) + 5 = max(48, 18) + 5 = 53 The project completion time is the maximum of the finish times of all terminal activities (H and L): Project Duration = max(EF(H), EF(L)) = max(56, 53) = 56 days. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer 56 to 56 Solution To find the project completion time, we perform a forward pass to find the Earliest Finish (EF) time for each activity: EF(A) = 6 EF(B) = EF(A) + 10 = 16 EF(C) = EF(A) + 14 = 20 EF(D) = EF(B) + 8 = 24 EF(E) = EF(C) + 12 = 32 EF(F) = EF(C) + 8 = 28 EF(G) = max(EF(D), EF(E)) + 16 = max(24, 32) + 16 = 48 EF(H) = max(EF(F), EF(G)) + 8 = max(28, 48) + 8 = 56 EF(K) = EF(B) + 2 = 18 EF(L) = max(EF(G), EF(K)) + 5 = max(48, 18) + 5 = 53 The project completion time is the maximum of the finish times of all terminal activities (H and L): Project Duration = max(EF(H), EF(L)) = max(56, 53) = 56 days.

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