(a) The network of a certain project is shown in the figure given below with the estimated time duration (in days) of various activities. Determine the following :
(i) Earliest event time
(ii) Latest event time
(iii) Earliest start and finish time of

Question

(a) The network of a certain project is shown in the figure given below with the estimated time duration (in days) of various activities. Determine the following :
(i) Earliest event time
(ii) Latest event time
(iii) Earliest start and finish time of each activity
(iv) Latest start and finish time of each activity
(v) Total float of each activity
(vi) Critical path of the network
(Assume the scheduled completion time of the project equal to the earliest event time of the last event)
20

(b) Prepare a detailed analysis of rate (₹ per sq. m) for a 25 mm thick cement concrete (1 : 2 : 4) floor with cement finishing coat. 15

(c) Sketch a typical diamond crossing and label all its components. Design a diamond crossing between two B.G. tracks crossing each other at an angle of 1 in 8·5. 15

UPSC Answer Check · Accepted Answer

Solve this multi-part technical problem by allocating approximately 40% time to part (a) CPM network analysis, 30% to part (b) rate analysis, and 30% to part (c) diamond crossing design. Begin with forward and backward pass calculations for the network, followed by systematic rate analysis using current DSR/CPWD norms, and conclude with geometric design calculations and neat sketching for the railway crossing.
- Part (a): Correct computation of EET and LET for all events using forward and backward pass method; identification of critical path with zero total float
- Part (a): Accurate calculation of EST, EFT, LST, LFT and total float for each activity with proper tabulation
- Part (b): Detailed rate analysis showing material quantities (cement, sand, aggregate), labour components, and cost breakdown per sq.m for 25mm thick CC 1:2:4 floor with finishing
- Part (b): Inclusion of wastage, water charges, overhead charges, and contractor profit as per standard practice; reference to CPWD/State PWD schedule of rates
- Part (c): Correct geometric design of diamond crossing for BG track with 1 in 8.5 crossing angle: calculation of nose of crossing, throat length, and check rails
- Part (c): Neat sketch showing all components: four noses, two obtuse angle crossings, two acute angle crossings, check rails, wing rails, and sleeper layout
- Part (c): Application of relevant formulae: sin α = 1/8.5, calculation of theoretical and actual nose of crossing, flaring of check rails

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding of CPM methodology (forward/backward pass, float concepts), rate analysis components, and diamond crossing geometry including all design formulae for 1 in 8.5 crossing angle	Shows basic understanding of CPM calculations and rate analysis but makes minor errors in diamond crossing geometry or omits some components in rate breakdown	Confuses EET/LET concepts, misses critical activities, or applies wrong formulae for crossing angle; rate analysis lacks essential components
Numerical accuracy	20%	10	All calculations precise: EET/LET correct to the day, rate analysis sums accurately with proper unit costs, diamond crossing dimensions (nose, throat, check rail flaring) computed correctly using sin α = 1/8.5	Minor arithmetic errors in some calculations (1-2 days off in network, 5-10% error in quantities, small dimensional errors) but method is sound	Major calculation errors, wrong use of formulae, or completely incorrect numerical values; failure to compute sin α or apply crossing angle correctly
Diagram quality	20%	10	Clear, scaled network diagram with activity durations labeled; neat diamond crossing sketch showing all four noses, check rails, wing rails, sleeper layout, and crossing angle; proper labeling of all components	Diagrams present but poorly scaled or with missing labels; network diagram lacks clarity in event numbering; diamond crossing sketch incomplete	Missing diagrams, illegible sketches, or failure to provide network/diamond crossing drawings as explicitly demanded
Step-by-step derivation	20%	10	Systematic presentation: tabular EET/LET computation with clear pass identification, detailed rate analysis with quantity calculations per unit, stepwise geometric derivation of crossing dimensions with formulae stated	Some steps shown but lacks systematic tabulation; rate analysis condensed; geometric derivation skips intermediate steps	No working shown, jumps to final answers, or presents only final results without methodology; illegible or disorganized presentation
Practical interpretation	20%	10	Relates critical path to project crashing decisions, justifies rate analysis assumptions with reference to CPWD/State PWD DSR 2022-23, explains practical significance of check rails and flaring in diamond crossing for Indian Railways BG standards	Brief mention of practical relevance without specific standards reference; generic statements about project management or construction	No practical context provided; purely theoretical treatment without connection to actual construction practice or railway engineering standards

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