A reliable method
Represent each change with a multiplier. For simple interest use principal × annual rate × years, and add principal only when the question asks for the final balance.
The common trap
A markup followed by a discount does not generally cancel. Profit as a percentage of cost differs from profit as a percentage of revenue.
Check the conclusion
Reconstruct the final amount from the recovered original. This checks both the arithmetic and whether you chose the correct percentage base.
Contrast the cases
A $100 cost marked up 35% becomes $135, then a 20% discount makes the price $108. Subtracting nominal percentages gives 15% and incorrectly predicts $115 because the second percentage has a new base. A $120 selling price at 20% profit on cost corresponds to cost $100, not $96. For interest, $500 at 4% simple annual interest over three years earns $60; a compound calculation would use changing principal.
Transfer and explain
Transfer: compute a 25% markup followed by a 20% discount on $80. The final price is $80 because the factors 1.25 and 0.8 multiply to one; explain why this cancellation is specific to these rates.
An item costing $300 is marked up by 35%, then its marked price is discounted by 20%. What is its final selling price in dollars?
- A 35% markup multiplies cost by 1.35.
- A 20% discount multiplies the marked price by 0.80.
- The combined factor is 1.08, giving $324.
Compare the other answer choices
Multiplies the change percentages and omits the retained cost.
Assumes markup and discount cancel.
Subtracts the rates instead of composing their changing bases.
Omits the final discount.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GMAT exam contentSiyavula Grade 10 mathematics foundation reference