Comparing Two Plastering Quotations with Penalty
A junior engineer must choose between two quotations for 12 mm cement plaster on 480 m² of external wall. Contractor P quotes ₹210 per m². P's rate excludes wastage, which is charged at 8% of the base amount, and GST is 18% on the base plus wastage. P promises completion in 18 days. Contractor Q quotes ₹245 per m², offers a 5% discount on the base amount, charges no wastage, and GST is 12% on the discounted amount. Q promises completion in 24 days. The work is on the critical path of a school building, and the department's penalty clause imposes ₹2,000 per day for every day beyond 20 days. Both contractors are technically qualified. The JE must put up a comparative statement, recommend one contractor, and answer the executive engineer's question: if the penalty clause were waived, how many days could Q take and still remain cheaper than P?
1. Compute the total payable to each contractor ignoring the penalty clause. Which is cheaper on cost alone?
Read the worked answer
P: base = 480 × 210 = ₹1,00,800. Wastage = 8% of 1,00,800 = ₹8,064. Subtotal = ₹1,08,864. GST = 18% of 1,08,864 = ₹19,595.52. Total = ₹1,28,459.52. Q: base = 480 × 245 = ₹1,17,600. Discount = 5% = ₹5,880. Net = ₹1,11,720. GST = 12% of 1,11,720 = ₹13,406.40. Total = ₹1,25,126.40. On cost alone, Q is cheaper by ₹3,333.12. The JE should show both workings in the comparative statement so the discount and wastage treatment are transparent.
2. Now include the penalty clause. Which contractor should be recommended, and by how much does the position change?
Read the worked answer
P finishes in 18 days, within the 20-day limit, so penalty = ₹0 and P's effective cost remains ₹1,28,459.52. Q finishes in 24 days, four days beyond 20, so penalty = 4 × ₹2,000 = ₹8,000. Q's effective cost = ₹1,25,126.40 + ₹8,000 = ₹1,33,126.40. P is now cheaper by ₹1,33,126.40 − ₹1,28,459.52 = ₹4,666.88. The recommendation should therefore be P, but the JE should record that the decision turns on the critical-path delay, not on the quoted rate. If the school deadline could absorb a four-day delay, the recommendation would reverse.
3. If the penalty clause were waived, what is the maximum number of days Q could take and still remain cheaper than P?
Read the worked answer
Q's base total is ₹1,25,126.40 and P's total is ₹1,28,459.52, so Q has a margin of ₹3,333.12. Each extra day beyond 20 costs ₹2,000. With 21 days, Q pays one day's penalty: 1,25,126.40 + 2,000 = ₹1,27,126.40, which is still below P. With 22 days, Q pays ₹4,000: ₹1,29,126.40, which exceeds P. So Q can take at most 21 days, i.e. one day beyond the 20-day limit. The answer must be stated as total days, not as extra days, because the question asks how many days Q could take.