Same peso amount, two different percentages — the question is always “percent of what?”
A store buys a bag for ₱480 and sells it for ₱600
Find the markup on cost.
The profit is ₱120, and markup is measured on the cost: 120 ÷ 480 = 25%. D is the margin (120 ÷ 600), measured on the selling price. Same ₱120 profit, two different percentages — the base decides which.
| Name | What it is | Here |
|---|---|---|
| cost | what the seller paid | ₱480 |
| selling price | what the buyer pays | ₱600 |
| profit | selling price − cost | ₱120 |
| loss | cost − selling price, when it sells for less | — |
600 − 480 = ₱120
The peso profit is never in doubt. Everything difficult in this topic is about which number it gets compared to.
120480 = 25%
profit ÷ cost
120600 = 20%
profit ÷ selling price
The denominator is the whole story. Markup divides by the smaller number, so it is always the bigger percentage. A question that says “profit is 25% of cost” and one that says “profit is 25% of the selling price” describe two different prices.
Default reading: “markup”, “profit rate” and “gain” are on cost unless the question names the selling price.
SP = C(1 + markup)
keep the cost, add the markup
SP = 480(1.25)
25% markup
SP = ₱600
back where we started ✓
sold at a 15% loss, cost ₱480
a loss is a minus
SP = 480(0.85)
you keep 85% of the cost
= ₱408
a ₱72 loss
If ₱600 already includes a 25% markup, the cost is 600 ÷ 1.25 = ₱480. Taking 25% off ₱600 gives ₱450, which is a different (and wrong) answer — the same trap as reversing a discount.
| Term | Measured against | Multiplier |
|---|---|---|
| markup | cost | 1 + rate |
| discount / markdown | list price | 1 − rate |
| loss | cost | 1 − rate |
| margin | selling price | — |
list ₱600, 10% off
the sale price
600(0.90) = ₱540
what the buyer pays
540 − 480 = ₱60 profit
still above cost
A discount is taken off the list price; the profit is still measured against the cost. Three different bases in one question is normal, which is why writing the three numbers down first pays off.
6% of 85 000
the rate on total sales
0.06 × 85 000
percent to decimal first
= ₱5 100
earned that period
With a ₱8 000 base plus 6%, the pay is 8 000 + 5 100 = ₱13 100. And “6% on sales above ₱50 000” applies the rate only to the excess: 0.06 × 35 000 = ₱2 100 — the same “beyond the first band” structure as a piecewise fare.
Two bands, run backwards: an agent earns 4% on the first ₱50,000 of sales and 6% on sales above that, and her commission is ₱5,000. The first band pays 0.04 × 50,000 = ₱2,000, so ₱3,000 came from the excess: 3,000 ÷ 0.06 = ₱50,000 above the band, and the sales were 50,000 + 50,000 = ₱100,000.
Backwards from a loss: an item sold for ₱1,105 at a 15% loss. Find the cost.
SP = C × 0.85
a loss keeps 85% of the cost
C = 1105 ÷ 0.85 = ₱1,300
check: 15% of 1,300 = 195, 1,300 − 195 = 1,105 ✓
What is different: the multiplier is below 1, so the cost comes out bigger than the selling price. Adding 15% to ₱1,105 gives ₱1,270.75, which fails the check.
A margin target: an item costs ₱360. What selling price gives a 25% margin?
profit = 0.25 × SP, so C = 0.75 × SP
the margin is a share of the selling price
SP = 360 ÷ 0.75 = ₱480
check: 120 ÷ 480 = 25% ✓
What is different: the base is the unknown price, so we divide.
360 × 1.25 = 450 is a 25% markup on cost. Its margin is only 90 ÷ 450 = 20%.
Two discounts in a row: 20% off, then a further 10% off a ₱2,500 list price.
0.80 × 0.90 = 0.72
multiply the multipliers
2500 × 0.72 = ₱1,800
the price paid
single discount = 1 − 0.72 = 28%
not 30%
What is different: the second 10% comes off ₱2,000, not ₱2,500, so the discounts do not add.
A dealer marks an item up 60% on cost, then sells it at 25% off the marked price, making a ₱90 profit. Find the cost.
SP = C × 1.60 × 0.75 = 1.2C
multiply the multipliers
profit = 1.2C − C = 0.2C = 90
a 20% profit on cost
C = 90 ÷ 0.2 = ₱450
check: marked 720, sold 540, profit 90 ✓
Run it backwards to set a price: an item costs ₱500, and the seller wants a 20% profit on cost even after 25% off. What marked price?
needed SP = 500 × 1.20 = 600
the profit target first
600 is 75% of the marked price
what is left after the discount
marked = 600 ÷ 0.75 = ₱800
check: 25% off 800 is 600 ✓
60% − 25% = 35% profit is the trap answer; the true profit is 20%. Likewise 500 × 1.45 = ₱725 just adds the two percents to the cost. And two items sold at the same price, one at a 20% gain and one at a 20% loss, do not break even: find each cost by dividing first.
The classic item chains a markup on cost with a discount on the marked price, then asks for the cost or the price. Write the multipliers in one line (C × 1.6 × 0.75), divide to go backwards, and check by running the story forward from your answer.
Find the selling price
An item costing ₱250 is marked up 40%. Find the selling price.
Markup runs on cost, so add 40% of 250 = ₱100 and the price is ₱350. B is the markup on its own, not the price. C comes from treating the 40% as a margin on the selling price instead of on cost.
