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Difficulty: HardProfit, Loss, and Markup

An artisanal coffee roasting company purchases unroasted green coffee beans at a cost of $12.00\$12.00 per kilogram. During the roasting process, moisture loss reduces the total weight of the coffee beans by 20%20\%. To set the regular retail price per kilogram of roasted beans, the company marks up the effective cost price per kilogram of roasted beans by 50%50\%. If the company sells the roasted beans at a promotional discount of 10%10\% off the regular retail price, what is the net profit percentage earned on the total cost of the unroasted green coffee beans?

Answer: 35 %

Answer

The net profit percentage earned on the total cost of the unroasted green coffee beans is 35%.
The correct calculation yields a total revenue of 16.20from0.80kgofroastedcoffeeproducedfrom1kgofgreencoffeepurchasedfor16.20 from 0.80 kg of roasted coffee produced from 1 kg of green coffee purchased for 12.00. This results in a net profit of 4.20,whichisexactly354.20, which is exactly 35% of the initial 12.00 cost.

Step-by-Step Solution

1
Calculate the effective cost per kilogram of roasted beans after weight loss.
Effective cost per kg of roasted beans = 12.00/(1−0.20)=12.00 / (1 - 0.20) = 15.00 per kg.
Because weight decreases by 20%, 1 kg of green beans yields 0.80 kg of roasted beans, raising the per-unit cost.
2
Calculate the regular retail price per kilogram of roasted beans.
Regular retail price = 15.00∗(1+0.50)=15.00 * (1 + 0.50) = 22.50 per kg.
The 50% markup is applied to the effective cost price of the roasted beans.
3
Calculate the promotional selling price after a 10% discount.
Discounted selling price = 22.50∗(1−0.10)=22.50 * (1 - 0.10) = 20.25 per kg.
The discount reduces the regular retail price by 10%.
4
Find total revenue generated from the yield of 1 kg of green coffee beans.
Total revenue = 0.80 kg * 20.25/kg=20.25/kg = 16.20.
1 kg of initial green beans produces 0.80 kg of sellable roasted product.
5
Calculate the net profit percentage based on the initial cost.
Net profit percentage = ((16.20−16.20 - 12.00) / 12.00)∗10012.00) * 100% = ( 4.20 / $12.00) * 100% = 35%.
Profit percentage is the net profit divided by the original total cost.

Key Concept

Multi-step profit calculation involving shrink/yield loss, markup, successive discounts, and base identification.
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Topics

Profit, Loss, and Markup

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