November 3, 2026

Test 15 – CPM Project Scheduling Applications

Question 1 ప్రశ్న 1

A water-main CPM network has independent starting activities A = 4 days and B = 6 days; C = 5 days follows A; D = 4 days follows B; and E = 3 days follows BOTH C and D. All links are zero-lag finish-to-start, with project time zero and no resource restrictions. Which is the controlling path and earliest project completion?

A A–C–E; 12 days. B Both A–C–E and B–D–E; 13 days. C B–D–E; 13 days. D B–D–E; 16 days.

Question 2 ప్రశ్న 2

Use this zero-lag CPM network: A = 4 and B = 6 days start independently; C = 5 days follows A; D = 4 days follows B; E = 3 days follows both C and D. The original project duration is 13 days. If only C increases from 5 to 7 days, what is the REVISED duration and critical path?

A 13 days; B–D–E remains critical. B 14 days; A–C–E becomes critical. C 15 days; both paths become critical. D 16 days; A–B–C–D–E becomes critical.

Question 3 ప్రశ్న 3

An AON pumping-station project has A = 5 and B = 4 days initially; C = 3 follows A; D = 6 follows B; E = 2 follows both C and D; F = 4 follows E. All links are zero-lag finish-to-start. If D is shortened from 6 to 3 days, what is the resulting EARLIEST project completion?

A 11 days, an improvement of 5 days. B 13 days, an improvement of 3 days. C 16 days, with no improvement. D 14 days, an improvement of 2 days.

Question 4 ప్రశ్న 4

A zero-lag AON network has A = 5 and B = 4 days as starting activities; C = 3 follows A; D = 6 follows B; E = 2 follows both C and D; F = 4 follows E. The backward pass uses the earliest project finish as its boundary. What are TOTAL FLOAT and FREE FLOAT of C?

A TF = 2 days; FF = 2 days. B TF = 0 days; FF = 2 days. C TF = 2 days; FF = 0 days. D TF = 6 days; FF = 2 days.

Question 5 ప్రశ్న 5

In a zero-lag AON network, independent activities A = 3 and B = 7 days are followed by C = 6 after A and D = 2 after B. E = 4 follows BOTH C and D, and F = 2 follows E. Which statement correctly identifies the critical paths?

A Only A–C–E–F is critical with 15 days. B Both A–C–E–F and B–D–E–F are critical with a 15-day completion. C Only B–D–E–F is critical with 17 days. D There are no critical paths because E has two predecessors.

Question 6 ప్రశ్న 6

A network contains independent A = 3 and B = 7 days, C = 6 after A, D = 2 after B, E = 4 after BOTH C and D, and F = 2 after E. The original duration is 15 days. If C is reduced from 6 to 3 days while everything else is unchanged, what is the revised project duration and controlling path?

A 12 days; A–C–E–F. B 13 days; both paths. C 15 days; B–D–E–F. D 18 days; B–D–E–F.

Question 7 ప్రశ్న 7

A reservoir project has initial A = 6 and B = 4 days; C = 5 follows A; D = 3 and F = 6 both follow B; E = 4 follows BOTH C and D; G = 2 follows BOTH E and F. All links are zero-lag finish-to-start. What are ES of G and earliest project completion?

A ES(G) = 15 days; project finish = 17 days. B ES(G) = 11 days; project finish = 13 days. C ES(G) = 10 days; project finish = 12 days. D ES(G) = 17 days; project finish = 19 days.

Question 8 ప్రశ్న 8

The CPM network has A = 6 and B = 4 as starting activities; C = 5 after A; D = 3 and F = 6 after B; E = 4 after C and D; G = 2 after E and F. Its original project duration is 17 days. If F's duration increases from 6 to 12 days, what is the revised completion and controlling path?

A 17 days; A–C–E–G remains the only critical path. B 19 days; B–D–E–G becomes critical. C 23 days; all activities become sequential. D 18 days; B–F–G becomes critical.

Question 9 ప్రశ్న 9

An AON project has A = 3 and B = 5 days initially; C = 4 after A; D = 6 after B; E = 3 after C and D; F = 2 after C; G = 4 after E and F. In the original schedule C finishes at time 7 and the project finishes at time 18. Suppose only C's ACTUAL finish shifts to time 10, with all remaining durations unchanged. What is the immediate scheduling consequence?

A E and F both retain their original earliest starts, and the project finishes at time 18. B The project necessarily finishes at time 21 because C finished three days late. C F's earliest start shifts from 7 to 10, while the project can still finish at time 18. D The project finishes at time 17 because F is accelerated.

Question 10 ప్రశ్న 10

A project has A = 3 and B = 5 days initially; C = 4 follows A; D = 6 follows B; E = 3 follows both C and D; F = 2 follows C; G = 4 follows both E and F. All links are zero-lag finish-to-start and the original finish is day 18. If D alone is shortened from 6 to 3 days, which result is correct?

A Project duration 18 days because C always controls E. B Project duration 15 days, an improvement of 3 days. C Project duration 14 days, an improvement of 4 days. D Project duration 16 days, an improvement of 2 days.

Question 11 ప్రశ్న 11

A water-treatment AON network has A = 4 and B = 3 days initially; C = 6 after A; D = 2 and F = 3 after B; E = 5 after BOTH C and D; G = 2 after BOTH E and F. Project duration is 17 days. B is actually started four days later than its original earliest start, but its duration remains 3 days. Assume no other changes. What is the revised project completion?

A 15 days. B 16 days. C 18 days. D 17 days.

Question 12 ప్రశ్న 12

Consider A = 4 and B = 3 days as independent starts; C = 6 follows A; D = 2 and F = 3 follow B; E = 5 follows C and D; G = 2 follows E and F. All links are zero-lag finish-to-start, and the original duration is 17 days. If the duration of critical Activity A increases from 4 to 6 days, what is the revised duration?

A 19 days. B 17 days. C 18 days. D 21 days.

Question 13 ప్రశ్న 13

A project has TWO independent terminal branches and a common zero-duration FINISH milestone reached only after both finish: A = 4 then C = 7 then E = 2; B = 5 then D = 5 then F = 2. All links are zero-lag finish-to-start. What is the LATEST START of terminal activity F when the backward pass uses the earliest project completion?

A 10 days. B 12 days. C 11 days. D 13 days.

Question 14 ప్రశ్న 14

AON activities A = 2 and B = 8 days start independently; C = 7 follows A; D = 1 follows B; E = 4 follows BOTH C and D. Initially both branches reach E at time 9 and the project finishes at time 13. If C is shortened to 5 days, which statement is correct?

A Project completion becomes 11 days, controlled by A–C–E. B Project completion remains 13 days, now controlled by B–D–E. C Project completion becomes 12 days, with both paths critical. D Project completion becomes 15 days because a critical activity was shortened.

Question 15 ప్రశ్న 15

An AON network has A = 6 and B = 5 days initially; C = 4 follows A; D = 7 follows B; E = 3 follows BOTH C and D; F = 2 follows E. The original project duration is 17 days. If B is shortened by 3 days, what is the new project duration and critical path?

A 17 days; B–D–E–F. B 14 days; B–D–E–F. C 16 days; both paths become critical. D 15 days; A–C–E–F.

Question 16 ప్రశ్న 16

A pump-house network has A = 4 and B = 7 days initially; C = 6 and F = 3 follow A; D = 2 follows B; E = 5 follows BOTH C and D; G = 2 follows BOTH E and F. Original duration is 17 days. If D increases from 2 to 4 days, what is the updated duration and controlling path?

A 18 days; B–D–E–G. B 17 days; A–C–E–G. C 19 days; A–F–G. D 20 days; B–D–E–G.

Question 17 ప్రశ్న 17

In a zero-lag AON project, A = 4 and B = 7 days start independently; C = 6 and F = 3 follow A; D = 2 follows B; E = 5 follows C and D; G = 2 follows E and F. The original duration is 17 days. If B increases from 7 to 8 days, which critical-path assessment is correct?

A Only B–D–E–G is critical and the project takes 18 days. B Only A–C–E–G remains critical and the project takes 17 days. C Both A–C–E–G and B–D–E–G become critical, with the project still taking 17 days. D All routes including A–F–G become critical and the project takes 17 days.

Question 18 ప్రశ్న 18

An AON project requires BOTH terminal activities F and G to be complete: A = 4 and B = 5 days initially; C = 6 follows A; D = 4 follows B; E = 3 follows BOTH C and D; F = 2 follows E; G = 7 follows B. Original project duration is 15 days. If G increases from 7 to 11 days, which result is correct?

A 15 days; A–C–E–F still controls. B 16 days; B–G becomes the controlling path. C 18 days; A–C–E–F and B–G are both critical. D 14 days; B–D–E–F controls.

Question 19 ప్రశ్న 19

A network requires BOTH terminal activities F and G: A = 4 and B = 5 days initially; C = 6 follows A; D = 4 follows B; E = 3 follows C and D; F = 2 follows E; G = 7 follows B. Original project duration is 15 days. If C is shortened by 2 days, what is the new project duration and critical path?

A 14 days; B–D–E–F. B 13 days; A–C–E–F. C 15 days; B–G. D 12 days; A–C–E–F.

Question 20 ప్రశ్న 20

A pipeline CPM network has A = 3 and B = 6 days as independent starts; C = 4 follows A; D = 2 follows B; E = 5 follows BOTH C and D; F = 4 follows C; G = 3 follows BOTH E and F. Its original duration is 16 days. If C increases to 5 days, which statement is correct?

A The duration becomes 17 days and only A–C–E–G is critical. B The duration becomes 15 days because F becomes critical. C The duration becomes 16 days and B–D–E–G alone remains critical. D The duration stays 16 days and BOTH A–C–E–G and B–D–E–G are critical.

Question 21 ప్రశ్న 21

A pipeline project has A = 3 and B = 6 days as starting activities; C = 4 follows A; D = 2 follows B; E = 5 follows BOTH C and D; F = 4 follows C; G = 3 follows BOTH E and F. The original duration is 16 days. If C increases from 4 to 6 days, what are the updated duration and sole controlling path?

A 16 days; B–D–E–G. B 18 days; A–C–F–G. C 17 days; A–C–E–G. D 19 days; both A–C–E–G and B–D–E–G.

Question 22 ప్రశ్న 22

A zero-lag CPM network has A = 5 and B = 4 days independently; C = 6 follows A; D = 5 follows B; E = 3 follows BOTH C and D. The original duration is 14 days and B–D–E has 2 days of path float. If B alone is delayed by 3 days with all durations otherwise unchanged, what is the revised project finish?

A 14 days; all noncritical delays are harmless regardless of size. B 15 days; B–D–E becomes the controlling path. C 17 days; the delay must be added to the original finish in full. D 12 days; B–D–E becomes shorter.

Question 23 ప్రశ్న 23

In an unconstrained zero-lag CPM schedule, two DISJOINT start-to-finish paths each last 18 days and no other path lasts as long. Only one path is shortened by 3 days; all other durations, relationships and resources are unchanged. What is the effect on earliest project completion?

A It becomes 15 days, because a critical path was shortened by 3 days. B It becomes 16.5 days, because the saving is shared equally. C It becomes 21 days, because both paths were originally critical. D It remains 18 days, because the other 18-day critical path still controls completion.

Question 24 ప్రశ్న 24

An AON project has two independent branches A = 4 followed by C = 6, and B = 5 followed by D = 5. Both C and D must finish before a COMMON final activity E = 4 days begins. All links are zero-lag finish-to-start, with no other terminal paths. Which single change reduces the earliest project completion by exactly TWO days?

A Shorten A by 2 days, leaving all other durations unchanged. B Shorten D by 2 days, leaving all other durations unchanged. C Shorten common activity E from 4 to 2 days. D Shorten E from 4 to 3 days.

Question 25 ప్రశ్న 25

A construction project initially has independent A = 3 and B = 4 days; C = 5 follows A; D = 2 follows B; and E = 3 follows BOTH C and D. All links are zero-lag finish-to-start. During method review, a NEW mandatory dependency is approved: D may start only after C is also complete. What is the revised earliest project duration and critical path?

A 13 days; A–C–D–E. B 11 days; A–C–E. C 12 days; B–D–E. D 15 days; A–B–C–D–E.

Answer Key సమాధానాల పట్టిక

Question 1 ప్రశ్న 1

Answer: C. B–D–E; 13 days. సమాధానం: C.
Question 2 ప్రశ్న 2

Answer: B. 14 days; A–C–E becomes critical. సమాధానం: B.
Question 3 ప్రశ్న 3

Answer: D. 14 days, an improvement of 2 days. సమాధానం: D.
Question 4 ప్రశ్న 4

Answer: A. TF = 2 days; FF = 2 days. సమాధానం: A.
Question 5 ప్రశ్న 5

Answer: B. Both A–C–E–F and B–D–E–F are critical with a 15-day completion. సమాధానం: B.
Question 6 ప్రశ్న 6

Answer: C. 15 days; B–D–E–F. సమాధానం: C.
Question 7 ప్రశ్న 7

Answer: A. ES(G) = 15 days; project finish = 17 days. సమాధానం: A.
Question 8 ప్రశ్న 8

Answer: D. 18 days; B–F–G becomes critical. సమాధానం: D.
Question 9 ప్రశ్న 9

Answer: C. F's earliest start shifts from 7 to 10, while the project can still finish at time 18. సమాధానం: C.
Question 10 ప్రశ్న 10

Answer: B. Project duration 15 days, an improvement of 3 days. సమాధానం: B.
Question 11 ప్రశ్న 11

Answer: D. 17 days. సమాధానం: D.
Question 12 ప్రశ్న 12

Answer: A. 19 days. సమాధానం: A.
Question 13 ప్రశ్న 13

Answer: C. 11 days. సమాధానం: C.
Question 14 ప్రశ్న 14

Answer: B. Project completion remains 13 days, now controlled by B–D–E. సమాధానం: B.
Question 15 ప్రశ్న 15

Answer: D. 15 days; A–C–E–F. సమాధానం: D.
Question 16 ప్రశ్న 16

Answer: A. 18 days; B–D–E–G. సమాధానం: A.
Question 17 ప్రశ్న 17

Answer: C. Both A–C–E–G and B–D–E–G become critical, with the project still taking 17 days. సమాధానం: C.
Question 18 ప్రశ్న 18

Answer: B. 16 days; B–G becomes the controlling path. సమాధానం: B.
Question 19 ప్రశ్న 19

Answer: A. 14 days; B–D–E–F. సమాధానం: A.
Question 20 ప్రశ్న 20

Answer: D. The duration stays 16 days and BOTH A–C–E–G and B–D–E–G are critical. సమాధానం: D.
Question 21 ప్రశ్న 21

Answer: C. 17 days; A–C–E–G. సమాధానం: C.
Question 22 ప్రశ్న 22

Answer: B. 15 days; B–D–E becomes the controlling path. సమాధానం: B.
Question 23 ప్రశ్న 23

Answer: D. It remains 18 days, because the other 18-day critical path still controls completion. సమాధానం: D.
Question 24 ప్రశ్న 24

Answer: C. Shorten common activity E from 4 to 2 days. సమాధానం: C.
Question 25 ప్రశ్న 25

Answer: A. 13 days; A–C–D–E. సమాధానం: A.

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