Question

A construction project consists of 7 activities. These activities, their connecting events, and the three PERT times (optimistic, likely, and pessimistic), in days, are listed in the table below. The project starts on 27th July 2026. Assuming no holidays for the entire duration of the project except 15th August 2026, the expected date of completion of the project will be August 2026 (mention the date in integer).

Activity	Connecting Events	Three PERT Times (in Days)
P	1 to 2	4 - 6 - 8
Q	1 to 3	5 - 6 - 13
R	2 to 5	6 - 8 - 22
S	2 to 3	8 - 11 - 14
T	3 to 5	2 - 4 - 12
U	3 to 4	4 - 8 - 18
V	4 to 5	5 - 7 - 15

Hint:

Find te = (a+4m+b)/6 for each activity, take the longest path 1-2-3-4-5 as the critical path (34 days), then count 34 working days from 27 July skipping the 15 August holiday.

Answer 1

Correct Answer: 30

Step 1: Understanding the Question.
The project has 5 events (1 to 5) connected by 7 activities, each with an optimistic (a), most likely (m), and pessimistic (b) time estimate. We need the expected completion date, given a start date of 27 July 2026 and one holiday on 15 August 2026.

Step 2: Key Formula.
The expected duration of each PERT activity is
\[ t_e = \frac{a + 4m + b}{6} \]
The project duration is the length of the longest path (critical path) from the start event to the end event, using these expected durations.

Step 3: Compute the expected time for each activity.
\[ t_e(P) = \frac{4+4(6)+8}{6} = \frac{36}{6} = 6 \]
\[ t_e(Q) = \frac{5+4(6)+13}{6} = \frac{42}{6} = 7 \]
\[ t_e(R) = \frac{6+4(8)+22}{6} = \frac{60}{6} = 10 \]
\[ t_e(S) = \frac{8+4(11)+14}{6} = \frac{66}{6} = 11 \]
\[ t_e(T) = \frac{2+4(4)+12}{6} = \frac{30}{6} = 5 \]
\[ t_e(U) = \frac{4+4(8)+18}{6} = \frac{54}{6} = 9 \]
\[ t_e(V) = \frac{5+4(7)+15}{6} = \frac{48}{6} = 8 \]

Step 4: List all paths from event 1 to event 5 and find their lengths.
1 to 2 to 5 (P + R): \(6+10=16\) days
1 to 2 to 3 to 5 (P + S + T): \(6+11+5=22\) days
1 to 2 to 3 to 4 to 5 (P + S + U + V): \(6+11+9+8=34\) days
1 to 3 to 5 (Q + T): \(7+5=12\) days
1 to 3 to 4 to 5 (Q + U + V): \(7+9+8=24\) days
The longest path is 1 to 2 to 3 to 4 to 5, taking 34 days. This is the critical path, so the project duration is 34 days.

Step 5: Count 34 working days from 27 July 2026, skipping the 15 August holiday.
Counting day 1 as 27 July, the 5 remaining days of July (27, 28, 29, 30, 31) take us to day 5. Day 6 is 1 August, so day \(n\) (for \(n \geq 6\)) falls on August date \((n-5)\), before accounting for the holiday.
Without any holiday, day 34 would fall on August \((34-5) = 29\).
But 14 August is day 19 (since \(19-5=14\)), so 15 August (day 20 in the naive count) is a holiday and is skipped, pushing every later day back by one.
So the actual day 34 (34th working day) falls on 30 August 2026.

Final Answer:
The expected date of completion of the project is 30 August 2026. \[ \boxed{30} \]