The Stationery Shop's Discount Decision
A stationery shop buys 120 notebooks at a list price of 50 taka each. The wholesaler offers two schemes. Scheme A: a trade discount of 20% on the list price, then a further 10% cash discount on the net amount. Scheme B: a flat discount of 28% on the list price with no further discount. The shop owner, Rafiq, plans to sell each notebook at a marked price of 60 taka and wants an overall profit of at least 15% on his actual purchase cost. He also notices that 8 of the notebooks are slightly damaged and can only be sold at 40 taka each. Rafiq must choose one scheme and set a single selling price for the undamaged notebooks. He wants the total profit on all 120 notebooks to be as close to 15% of cost as possible without falling below it.
1. Compute the effective purchase cost per notebook under each scheme and state which scheme gives the lower cost.
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Scheme A: First discount 20% of 50 = 10, so net price = 40. Second discount 10% of 40 = 4, so final price = 36 taka.
Scheme B: Discount 28% of 50 = 14, so final price = 50 − 14 = 36 taka.
Both schemes give exactly the same cost, 36 taka per notebook. This happens because successive discounts of 20% and 10% equal a single discount of 20 + 10 − (20×10)/100 = 28%.
So the choice cannot be made on cost alone; Rafiq must look at other factors (payment timing, damage handling). Cost per notebook = 36 taka under either scheme.
2. With the 8 damaged notebooks sold at 40 taka each, find the selling price per undamaged notebook that yields exactly 15% profit on total cost.
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Total cost = 120 × 36 = 4320 taka.
Target total revenue for 15% profit = 4320 × 1.15 = 4968 taka.
Revenue from 8 damaged notebooks = 8 × 40 = 320 taka.
Remaining revenue needed from 112 undamaged notebooks = 4968 − 320 = 4648 taka.
Selling price per undamaged notebook = 4648 ÷ 112 = 41.5 taka.
Check: 112 × 41.5 = 4648; plus 320 = 4968; profit = 4968 − 4320 = 648; 648/4320 = 15%. Correct.
Note this is below the planned marked price of 60 taka, so a discount from the marked price is possible while still hitting the target.
3. Rafiq wants a round selling price in whole taka for the undamaged notebooks that keeps profit at or just above 15%. What price should he set, and what is the resulting profit percentage?
Read the worked answer
From the previous task, exactly 15% needs 41.5 taka. A whole-taka price must be at least 41.5, so the smallest whole number is 42 taka.
Revenue = 112 × 42 + 8 × 40 = 4704 + 320 = 5024 taka.
Profit = 5024 − 4320 = 704 taka.
Profit percentage = 704/4320 × 100 ≈ 16.30%.
If he set 41 taka: revenue = 112 × 41 + 320 = 4592 + 320 = 4912, profit = 592, which is 13.70% - below target. So 42 taka is the correct minimum whole-taka price, giving about 16.3% profit, close to but not below 15%.