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GATE 2026 AR — Planning – Question 46

Project Management and Professional Practice · Construction project management techniques e.g. PERT, CPM · 2 marks · Numerical answer

A PERT project starts 27 July 2026. Activities and (optimistic, most likely, pessimistic) days are P 1→2(4, 6, 8), Q 1→3(5, 6, 13), R 2→5(6, 8, 22), S 2→3(8, 11, 14), T 3→5(2, 4, 12), U 3→4(4, 8, 18), V 4→5(5, 7, 15). All days are working except 15 August 2026. Give the completion date in August as an integer.

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Correct answer: 30 to 30

Explanation

PERT means (a+4m+b)/6 are P 6, Q 7, R 10, S 11, T 5, U 9, V 8 days. Event 3 cannot occur until max(7, 6+11)=17; event 4 is 26; event 5 is max(6+10, 17+5, 26+8)=34. Thus critical path P–S–U–V takes 34 working days. Counting 27 July as day 1 gives 29 August before the holiday allowance. Excluding 15 August adds one day, so completion is 30 August.

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