Profit, Loss, Markup, and Commission
Track the cost, marked price, and selling price separately before applying percentages.
Profit, Loss, Markup, and Commission
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Every business percentage needs a clearly identified base
Cost price is what the seller paid. Marked price is the displayed price before discounts. Selling price is what the buyer actually pays.
Profit = selling price − cost priceProfit rate = profitcost priceMarkup is added to cost; a discount is removed from marked price; commission is usually a percentage of sales.
Name all three prices
Do not treat cost, marked price, and selling price as interchangeable. Write them down before calculating.
Percentages use different bases
Profit rate usually uses cost, discount uses marked price, and commission uses total sales.
Build a multiplier chain in the correct order
A 40% markup followed by a 25% discount becomes cost×1.40×0.75. For a target profit, work backward from the required selling price before undoing the discount.
Why it works
Percent changes are applied to the amount existing at that stage. A discount after a markup acts on the marked price, not directly on the original cost.
Five forms you should recognize
Problem: An item costs ₱750 and sells for ₱900. Find the profit rate.
Profit = 900−750 = 150; 150750 = 20%Why: The usual profit rate is compared with the seller’s cost.
Problem: A ₱2,000 item is marked up 40%, then discounted 25%.
2,000(1.40)(0.75) = ₱2,100Why: Each percentage acts on the price produced by the previous step.
Problem: An item sells for ₱1,440 at a 20% profit. Find its cost.
Cost = 1,4401.20 = ₱1,200Why: The selling price represents 120% of cost.
Problem: An agent receives ₱12,000 plus 3% of ₱200,000 sales.
12,000 + 0.03(200,000) = ₱18,000Why: Total earnings include both fixed salary and sales-based commission.
Problem: Fifty ₱80 mugs are bought; five break. Find the price per remaining mug for a 12.5% overall profit.
50(80)(1.125)45 = ₱100Why: The target revenue must recover the cost of every mug, including those that cannot be sold.
Check before you commit
- Dividing profit by selling price when the question asks for profit rate based on cost
- Subtracting a discount directly from cost instead of marked price
- Adding successive percentages that use different bases
- Ignoring damaged or unsold inventory when computing total investment
- Treating commission as the agent’s total salary when a base salary is also given
- Working forward when a target-profit problem is easier to solve backward
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Profit, Loss, Markup, and Commission FAQ
What is the difference between markup and profit?
Markup is the amount added to cost to set a marked price; actual profit depends on the final selling price after any discounts and expenses.
Why is profit percentage usually based on cost?
It measures the return relative to the seller’s investment in the item.
How do I solve a target-profit price problem?
Find the selling price required for the target profit, then reverse any planned discount to obtain the marked price.
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