(a) A contractor intends to bid for erecting a statue at a square in an urban area. The various activities of the entire project are given below :

| Activity | Activity Name | Remark |
|----------|---------------|--------|
| A | Make statue | Starti

Question

(a) A contractor intends to bid for erecting a statue at a square in an urban area. The various activities of the entire project are given below :

| Activity | Activity Name | Remark |
|----------|---------------|--------|
| A | Make statue | Starting activity |
| B | Lay foundation | Starting activity |
| C | Construct platform | Follows B (starts after laying foundation) |
| D | Erect statue | Finishing activity and follows A and C |

The project is expected to take 18 days to complete having a variance of 4 days. Determine in how many days the contractor would expect the project to be completed with a probability of 99%. For probability of 98.93%, the corresponding normal deviate Z value is +2.3 and for probability of 99.18%, Z value is +2.4. Further, if the contractor intends to complete the project in 17 days by crashing the activities, determine how much total project cost would the contractor expect. The normal and crash duration, and associated cost are given in the table below for various activities :

| Activity | Normal Activity | | Crash Activity | |
|----------|-----------------|---|----------------|---|
| | Duration (in days) | Cost (in ₹) | Duration (in days) | Cost (in ₹) |
| A | 8 | 6,000 | 5 | 9,000 |
| B | 4 | 2,000 | 3 | 4,000 |
| C | 8 | 5,000 | 7 | 5,500 |
| D | 6 | 3,000 | 3 | 7,500 |

For the entire project, the indirect cost is ₹ 500 per day. (20 marks)

(b) (i) A taxi driver was fined for crossing the traffic signal at right-angled road intersection. He claimed that the signal was faultily designed and the duration of amber light is not sufficient. Using the following data, verify the correctness of the driver's claim :

Road width at intersection = 20 m
Speed limit at road = 60 kmph
Amber light duration = 4.0 s
Comfortable deceleration = 3.0 m/s²
Car length = 4.0 m
Perception reaction time = 1.2 s (10 marks)

(ii) Explain with sketches how the subsurface drainage system is provided to lower the water table in road. (5 marks)

(c) Calculate the maximum number of wagons of weight 80 tonnes each that can be pulled by a locomotive having hauling capacity of 16 tonnes. The weight of the locomotive is 100 tonnes and the train has to run at a speed of 60 kmph on a straight level BG track. Assume rolling resistance of wagon and locomotive as 1.6 kg/tonne and 2.0 kg/tonne respectively.

Also, calculate the hauling capacity of the locomotive required if the train has to climb a gradient of 1 in 150 in 1° curve. (15 marks)

UPSC Answer Check · Accepted Answer

Begin by identifying the critical path and calculating expected project duration with probability for part (a), then verify amber light timing using kinematic equations for part (b)(i), sketch subsurface drainage for (b)(ii), and finally compute hauling capacity and gradient resistance for part (c). Allocate approximately 40% time to part (a) due to its 20 marks and complexity involving PERT and crashing, 30% to part (b) combined, and 30% to part (c). Present all calculations systematically with clear labeling of each sub-part.
- Part (a): Identify critical path (B-C-D), calculate expected duration (18 days), determine Z-value for 99% probability (interpolate to Z=2.37), compute completion time (~22.7 days), perform crashing analysis by cost slope to reduce duration to 17 days at minimum additional cost including indirect costs
- Part (b)(i): Calculate stopping sight distance using perception-reaction time and braking distance, determine safe amber time using dilemma zone concept (ISD = v*t + v²/2a + vehicle length), compare with given 4.0s amber duration to verify driver's claim
- Part (b)(ii): Sketch longitudinal section showing perforated pipe, filter media, outlet structure, and lowered water table position with proper labeling for subsurface drainage in road construction
- Part (c): Calculate total train resistance on level track (rolling resistance of locomotive + wagons), equate to hauling capacity to find maximum wagons (16), then compute required hauling capacity for 1 in 150 gradient with 1° curve using Ruling Gradient formula including curve resistance (0.04% per degree)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies critical path B-C-D for (a), applies PERT probability formula with proper Z-interpolation, uses correct dilemma zone/amber time formula for (b)(i), and applies Indian Railways standard formulas for gradient and curve resistance in (c) including 0.04% per degree curve resistance	Identifies correct critical path but makes minor errors in probability calculation or crashing logic; applies basic kinematic equations for amber time but misses dilemma zone nuance; computes basic hauling capacity but omits curve resistance or uses incorrect gradient formula	Wrong critical path identification (A-D or others), incorrect application of normal distribution for probability, uses simple speed-distance-time for amber verification without deceleration, or confuses hauling capacity with tractive effort without resistance calculations
Numerical accuracy	20%	10	Precise calculations: Z=2.37 for 99% probability yielding ~22.7 days, minimum crashing cost with correct cost slopes (A:1000/day, B:2000/day, C:500/day, D:1500/day) selecting C and A, total cost ₹23,500; amber time calculation showing 4.0s is insufficient; 16 wagons on level, ~23 tonnes hauling capacity for gradient	Correct methodology but minor arithmetic errors in interpolation, crashing cost summation, or unit conversions (kmph to m/s); reasonable wagon count with slight resistance calculation errors; gradient calculation missing one component	Major calculation errors: wrong Z-value application, incorrect cost slope calculations leading to wrong crashing decisions, unit conversion errors (kmph to m/s), or order-of-magnitude errors in hauling capacity due to resistance formula mistakes
Diagram quality	15%	7.5	Clear AOA or AON network diagram for (a) showing all activities with durations and dependencies; neat labeled sketch for (b)(ii) showing pipe, gravel envelope, impervious layer, original and lowered water table, and outlet; well-organized tabular presentation for crashing analysis	Basic network diagram without clear node numbering or missing some dependencies; simple drainage sketch missing some labels or layers; tables present but not optimally formatted	Missing network diagram, confusing hand-drawn sketches without labels, or no diagram for (b)(ii) despite explicit requirement; illegible or poorly organized presentation that hinders evaluation
Step-by-step derivation	25%	12.5	Systematic presentation: for (a) shows ES/EF/LS/LF calculations, variance along critical path, Z-formula Te = T + Zσ with interpolation shown, cost slope table, crashing steps with iteration; for (b)(i) derives ISD formula with substitution; for (c) shows resistance balance equation and gradient resistance derivation	Shows key steps but skips some intermediate calculations like ES/EF table or assumes Z-value without interpolation; presents final formulas with values substituted but limited derivation shown; basic equation setup for hauling capacity	Jumps to final answers without showing workings, missing critical steps like critical path identification method, no formula statement before substitution, or disorganized calculation sequence that prevents verification
Practical interpretation	20%	10	Interprets 99% probability completion time as conservative bid estimate with 1% risk; explains crashing decision considers both direct and indirect costs (₹500/day); concludes amber time is insufficient based on calculated safe time (>4s), validating driver's claim; relates hauling capacity to Indian Railways BG standards and operational safety margins	States final answers without contextual interpretation; basic conclusion on crashing being cost-effective or not; simple valid/invalid statement for driver's claim without engineering justification; standard answer for railway capacity without operational context	No interpretation of results, fails to conclude whether project should be bid or crashed, no verdict on driver's claim validity despite calculation, or ignores practical implications of gradient hauling capacity for train operations

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