Arithmetic
Profit, Loss and Discount formulas
At a glance
Profit % = (SP − CP) / CP × 100 SP = CP × (1 + p/100) MP = CP × (1 + m/100) SP = MP × (1 − d/100) markup m, discount d → profit = m − d − md/100 MP/CP = (100 + p)/(100 − d) discounts a, b → single = a + b − ab/100 false weight w for 1000 → gain = (1000 − w) / w buy x get y free → discount = y / (x + y) CP of n = SP of x → profit = (n − x) / x same SP, ±r% → loss = r²/100 %
Cost price, selling price, profit
Profit = SP − CP Profit % = Profit / CP × 100 SP = CP × (1 + p/100) CP = SP ÷ (1 + p/100) Loss of l%: SP = CP × (1 − l/100)
Shortcut: Think in factors. 15% profit is SP = CP × 1.15; 10% loss is SP = CP × 0.9. To go back from SP to CP, divide by the factor.
Marked price and discount
MP = CP × (1 + m/100) SP = MP × (1 − d/100) SP / CP = (1 + m/100) × (1 − d/100) Profit % = m − d − md/100 Want p% profit after d% off: MP / CP = (100 + p) / (100 − d)
Shortcut: Markup then discount is just two successive changes: +m% then −d%. Use m − d − md/100: 40 − 20 − 800/100 = 12%.
Successive discounts
single discount = a + b − ab/100 20% then 10%: 20 + 10 − 200/100 = 28% Price paid = MP × (1 − a/100) × (1 − b/100) × …
False weights: the dishonest dealer
Gain % = (true weight − false weight) / false weight × 100 800 g for 1 kg: 200 / 800 = 25% With a markup m%: SP / CP = (1 + m/100) × 1000 / w
Shortcut: 10% above cost with a 900 g weight: 1.1 × 1000/900 = 11/9 = 1.2222, a 22.22% gain. Never add 10% and 11.11%.
Buy x, get y free
Buy x, get y free → discount = y / (x + y) SP / CP = (1 + m/100) × x / (x + y)
Cost of some articles = price of others
CP of n articles = SP of x articles Profit % = (n − x) / x × 100 (a loss if x > n)
Same selling price, one profit, one loss
Same SP, r% profit on one and r% loss on the other: overall loss % = r² / 100 (always a loss)
Formulas stick when you use them
The Profit, Loss and Discount lesson has worked problems and quick checks for every formula here. Free to start.
Start free