Bisi Prints: Reams, VAT and a 4:3:2 Sharing Ratio
Bisi Prints, a three-partner publishing firm in Ibadan, has won a contract to supply 12,500 copies of a 12-page workbook to a state ministry of education. Each copy is printed on 3 sheets of paper, each sheet carrying four pages printed on both sides, and the firm always adds 4% extra sheets for waste and spoilage. Paper is sold only in reams of 500 sheets at ₦6,400 per ream. Printing and ink cost ₦80 per copy, stitching and trimming cost ₦1,200 per 50 copies, and delivery to the ministry's store costs a flat ₦800. The ministry pays ₦480 per copy and, in addition, 7.5% VAT, which Bisi Prints must remit in full to the revenue service. The partners agreed that 10% of any profit goes into a reserve fund, and the remainder is shared between Bisi, Tunde and Ngozi in the ratio 4:3:2. Before accepting the contract the partners set themselves a target net margin of at least 68% of contract income, VAT excluded.
1. How many reams of paper must Bisi Prints order, and what will the paper cost?
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Sheets per copy. The workbook has 12 pages and each sheet carries 4 pages, so each copy uses 12 ÷ 4 = 3 sheets.
Total sheets before waste. 12,500 copies × 3 sheets = 37,500 sheets.
Add 4% waste. 37,500 × 0.04 = 1,500 sheets, giving 37,500 + 1,500 = 39,000 sheets.
Convert to reams. 39,000 ÷ 500 = 78 reams exactly. Because reams cannot be bought in fractions, 78 is already a whole number, so no rounding up is needed.
Cost. 78 × ₦6,400 = ₦499,200 (check: 78 × 64 = 4,992, then add two zeros).
Judgement check. Ordering only 77 reams gives 38,500 sheets, which is 500 sheets short of the waste-inclusive requirement, so the job would stall before the last batch. The answer must be 78 reams, not the 75 reams that a candidate who forgets the waste allowance would obtain (37,500 ÷ 500 = 75).
2. Work out the total production cost, the contract income excluding VAT, and the profit. Express the profit in standard form and decide whether the 68% margin target is met.
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Build up the cost.
- Paper: 78 × ₦6,400 = ₦499,200
- Printing and ink: 12,500 × ₦80 = ₦1,000,000
- Binding: 12,500 ÷ 50 = 250 batches; 250 × ₦1,200 = ₦300,000
- Delivery: ₦800
Total cost = 499,200 + 1,000,000 + 300,000 + 800 = ₦1,800,000.
Income. The VAT is collected on behalf of the revenue service and is not the firm's income, so it is excluded: 12,500 × ₦480 = ₦6,000,000. (The ₦450,000 VAT is added to the ministry's bill and remitted; treating it as income would overstate profit by ₦450,000.)
Profit. 6,000,000 − 1,800,000 = ₦4,200,000 = ₦4.2 × 10⁶ in standard form.
Margin test. 4,200,000 ÷ 6,000,000 × 100 = 70%. The target was 68%, so it is met, with 2 percentage points to spare. If a candidate wrongly counted VAT as income, the margin would appear as (6,450,000 − 1,800,000) ÷ 6,450,000 ≈ 72%, which is a different answer and a false comfort.
3. Show how the profit is shared among the three partners after the reserve fund is set aside.
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Reserve first. 10% of ₦4,200,000 = ₦420,000 set aside.
Shareable profit. 4,200,000 − 420,000 = ₦3,780,000.
One part of the ratio. Ratio 4:3:2 gives 4 + 3 + 2 = 9 parts, so one part = 3,780,000 ÷ 9 = ₦420,000. (The reserve happens to equal one part here, which is a useful check, not a coincidence to rely on.)
- Bisi: 4 × 420,000 = ₦1,680,000
- Tunde: 3 × 420,000 = ₦1,260,000
- Ngozi: 2 × 420,000 = ₦840,000
Check. 1,680,000 + 1,260,000 + 840,000 = ₦3,780,000, and adding the reserve gives ₦4,200,000. A common error is to apply the ratio to the whole profit, which would give Bisi 4/9 × 4,200,000 ≈ ₦1,866,667 and leave the reserve unfunded.