Quantitative Aptitude / Numerical Ability - Choosing Between Two Quotations Before the Financial Year Closes
A branch office must buy 60 first-aid kits and 45 uniforms before 31 March. Two quotations are on file. Vendor A quotes ₹480 per kit and ₹900 per uniform, offers a flat 12% discount on the total value of the order, and charges GST at 5% on the discounted value. Vendor B quotes ₹500 per kit and ₹850 per uniform, runs a 'buy five kits, get one free' scheme, gives no discount on uniforms, and states that its quoted prices are inclusive of all taxes. The branch has a sanctioned budget of ₹62,000 for the purchase, and the rules do not permit splitting the order between vendors or buying more than the stated requirement. The purchase committee must also record how much GST is being paid under the chosen quotation, because tax paid is reported separately in the branch's annual account.
1. Compute the total landed cost and the GST component under Vendor A's quotation.
Read the worked answer
Step 1 - pre-discount value.
- Kits: 60 × ₹480 = ₹28,800
- Uniforms: 45 × ₹900 = ₹40,500
- Total: ₹69,300
Step 2 - discount. 12% of ₹69,300 = ₹8,316, so the discounted value is 69,300 − 8,316 = ₹60,984. (Shortcut: 69,300 × 0.88.)
Step 3 - GST. 5% of ₹60,984 = ₹3,049.20, giving a landed cost of 60,984 × 1.05 = ₹64,033.20.
Judgement points. The discount applies to the whole order value, not separately to kits and uniforms, so the arithmetic must be done on the combined figure. GST is charged on the discounted value, not on ₹69,300 - applying 5% to the pre-discount total would wrongly add ₹3,465 and inflate the cost to ₹64,449, an error of nearly ₹416. The ₹3,049.20 is the figure the committee must report as tax paid if this quotation is chosen.
2. Compute Vendor B's total payable, compare the two quotations, and rule on the ₹62,000 budget.
Read the worked answer
Step 1 - kits under the scheme. Pay for 5, get 1 free, so every 6 kits cost the price of 5. For 60 kits the branch pays for 60 × 5/6 = 50 kits: 50 × ₹500 = ₹25,000. It receives exactly 60 kits - ten free units - with nothing left over, so no adjustment for surplus stock is needed.
Step 2 - uniforms. 45 × ₹850 = ₹38,250; the scheme covers kits only, so no free units arise here.
Step 3 - total. 25,000 + 38,250 = ₹63,250, and because quoted prices are tax-inclusive, no GST is added.
Comparison. B is cheaper by 64,033.20 − 63,250 = ₹783.20. Under B the entire ₹63,250 is treated as tax-inclusive consideration, so the tax component is embedded rather than separately billed - the committee should obtain B's tax break-up for its records rather than assume nil.
Budget ruling. Both quotations exceed ₹62,000, by ₹2,033.20 (A) and ₹1,250 (B). Since splitting the order or buying extra is barred, the branch cannot award on either quotation within sanction. The correct course is to seek revised quotations or a budget enhancement before 31 March, not to buy short of the stated requirement.
3. By how much would Vendor A have to reduce its uniform rate for A to become cheaper than B? Round sensibly.
Read the worked answer
Set up the inequality. Let the uniform rate be ₹u. Vendor A's landed cost is (28,800 + 45u) × 0.88 × 1.05, and this must fall below B's ₹63,250.
Combine the multipliers. 0.88 × 1.05 = 0.924.
Solve. (28,800 + 45u) × 0.924 < 63,250 → 28,800 + 45u < 63,250 ÷ 0.924 = ₹68,442.64 → 45u < ₹39,642.64 → u < ₹880.95
Interpretation. At any uniform rate of ₹880 or less, Vendor A's total drops below ₹63,250 and A becomes the cheaper quotation; at ₹881 it is still marginally dearer. So the reduction needed is about ₹900 − ₹880 = ₹20 per uniform, roughly 2.2%.
Check with u = ₹880: 45 × 880 = ₹39,600; plus ₹28,800 = ₹68,400; × 0.924 = ₹63,201.60, which is indeed below ₹63,250.
Judgement. A ₹20-per-uniform concession is a small ask, so the committee can negotiate on a narrow margin rather than reopening the whole tender - but even after the concession the cost stays above the ₹62,000 sanction, so a budget enhancement is still required.