Two Quotations, One Shrinking Class Fund
A PRT has Rs 1,800 sanctioned from the class fund to buy chart paper for a science corner. The requirement is 240 sheets for the corner plus a further 20 sheets that must be held back for annual-day banners - 260 sheets in all. Vendor A: Rs 9 per sheet; 8% discount on the bill if the bill before delivery is Rs 1,500 or more; delivery free above Rs 1,500, otherwise Rs 60. Vendor B: Rs 8 per sheet; 5% discount only if more than 300 sheets are purchased; delivery Rs 120 flat; and 10 free sheets for every 100 sheets purchased. Vendor A can deliver in one working day. Vendor B needs two working days. The science corner is to be inaugurated tomorrow, and the head has asked for the exact shortfall, if any, in writing.
1. Compute the cost of meeting the 260-sheet requirement from each vendor, including free sheets, and state which quotation is cheaper in total and which is cheaper per usable sheet.
Read the worked answer
Vendor A: bill = 260 × 9 = Rs 2,340, which clears the Rs 1,500 threshold. Discount = 8% of 2,340 = Rs 187.20 → Rs 2,152.80. Delivery free (bill above Rs 1,500). Sheets received = 260. Cost per usable sheet = 2,152.80 ÷ 260 = Rs 8.28.
Vendor B: pay for 260 sheets = 260 × 8 = Rs 2,080. Purchase is not above 300, so the 5% discount does not apply - this is the step most likely to be got wrong, because '260' looks like a big order. Free sheets = 10 per 100 purchased = 26. Total received = 286. Add delivery Rs 120 → Rs 2,200 for 286 sheets. Cost per usable sheet = 2,200 ÷ 286 = Rs 7.69 (approx).
Conclusion to report: Vendor A is cheaper in total by Rs 47.20 (2,200 − 2,152.80) for the exact quantity needed. Vendor B is cheaper per sheet, but only because it forces 26 surplus sheets on the school. If the surplus can be stored and used next term, B is the better buy; if not, the Rs 47.20 saved with A is real money and the surplus is not.
2. Using the Rs 1,800 cap, find the maximum quantity obtainable from each vendor and state which vendor actually supplies more usable sheets within the budget.
Read the worked answer
Vendor A: with the 8% discount applying from 167 sheets upward, effective rate = 9 × 0.92 = Rs 8.28 per sheet. Solve 8.28n ≤ 1,800 → n ≤ 217.39, so n = 217 sheets. Check: 217 × 9 = 1,953; less 8% (156.24) = Rs 1,796.76, within budget. At 218 sheets the bill is 1,962, less 156.96 = Rs 1,805.04 - over. So 217 sheets, no free sheets.
Vendor B: cost = 8n + 120 ≤ 1,800 → 8n ≤ 1,680 → n ≤ 210. So 210 purchased, bill 1,680 + 120 = Rs 1,800 exactly. Free sheets = 10 per 100 = 21. Total received = 231 sheets.
Usable after the 20-sheet banner reserve: A gives 217 − 20 = 197 for the corner; B gives 231 − 20 = 211.
Recommendation: within the cap, Vendor B supplies 14 more usable sheets, even though its unit rate only wins because of the free-sheet scheme. Against the 240-sheet target, both fall short - B by 29 sheets, A by 43 - and that shortfall is what must be stated in writing to the head rather than absorbed silently.
3. Vendor B needs two working days but the corner opens tomorrow. Recommend a course of action that respects the budget and the deadline, and state the risk in your recommendation.
Read the worked answer
Recommendation: split the order rather than choose one vendor.
- Buy the minimum needed for the inauguration from Vendor A today - say 60 sheets at the discounted rate ≈ Rs 496.80 (60 × 9 = 540, less 8% = 496.80; the Rs 1,500 delivery threshold is not met, so add Rs 60 → Rs 556.80).
- Place the remaining requirement with Vendor B for delivery in two days.
Why not simply buy everything from A: A costs Rs 2,152.80 for exactly 260 sheets, but that exceeds the Rs 1,800 cap, so it cannot be done without fresh sanction. Why not wait for B: the inauguration cannot be postponed for a paper order, and the head has asked for a written position today.
The risk to state in writing: a split order pays two delivery charges and forfeits B's 5% discount on the first tranche, so the combined cost is higher than either single-vendor figure. That extra cost is the price of the deadline and should be shown as a separate line to the head, not hidden inside a single total.
What to avoid: quietly buying 260 sheets from A and presenting a bill above sanction - a small, common, and avoidable audit problem.