A reliable method
Write the multiplier for the change. Divide a final amount by that multiplier to reverse it. In a ratio, add the parts before finding the value of one part.
The common trap
Subtracting the same percentage from a discounted amount does not reverse the discount. Currency rates need a clear direction and unit.
Make the connection
Direct proportion keeps a quotient constant; inverse proportion keeps a product constant. Check which relationship the context actually supports.
Reverse the multiplier, not the percentage
A 20% discount takes an original 100 dollars to 80. Adding 20% of 80 gives 96, so it does not recover the original amount. Divide the sale price by 0.8 instead. In a ratio 3:5, the first part is three eighths of the total, not three fifths. A 40-litre mixture therefore contains 15 litres of the first component. For inverse proportion, four workers completing a fixed job in six hours represents 24 worker-hours; eight equally productive workers would take three hours. State the model assumption before using that inverse relationship.
Transfer, explain and check
A price becomes 132 after a 10% increase. Recover 120 by dividing by 1.1. For a separate direct-proportion recipe, doubling servings doubles ingredients; explain why that differs from doubling workers on a fixed job.
A jacket costs 48 dollars after a 20% discount. What was its original price in dollars?
- The sale price is 80% of the original.
- Divide by 0.8 rather than adding 20% of the sale price.
- The original price is 60 dollars.
Compare the other answer choices
Return the sale price rather than the original price.
Add 20 percent of the discounted price instead of undoing the discount.
Apply another 20 percent 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.
Cambridge IGCSE Mathematics 0580