Example 1
A bag costs $68 after a 15% discount. Find its original price.
- The final price is 85% of the original: 0.85 × original = 68.
- Original = 68 ÷ 0.85 = $80.
- Check: 15% of $80 is $12, leaving $68.
Home › Subjects › O-Level Elementary Maths (E-Maths) › Percentage
Percentages: reverse percentages and successive changes
The most important part of a percentage calculation is its base. Ask ‘percentage of what?’ before reaching for a calculator. A price before a discount, a price after a discount and a profit percentage can all use different bases.
Choose the method
Convert an increase of r% to the multiplier 1 + r/100; a decrease uses 1 - r/100. This keeps the original amount visible in the calculation.
To reverse a change, divide by the multiplier. Subtracting the same percentage from the final value uses the wrong base.
For successive changes, multiply the factors in order. For percentage change, use (final - original)/original × 100%. Keep unrounded values until the final answer.
Worked examples
Example 2
A value of 200 increases by 10%, then decreases by 10%. Find the final value and overall percentage change.
- Use the new base for the second change: 200 × 1.10 × 0.90 = 198.
- Overall change = (198 - 200)/200 × 100% = -1%.
- The changes do not cancel: the decrease is taken from 220, not 200.
Try it yourself
A population increases from 800 to 920. Find the percentage increase.
Show the worked answer
- Increase = 920 - 800 = 120.
- Percentage increase = 120/800 × 100% = 15%. The denominator is the original population.
Common mistakes
- A profit margin uses selling price as the base; profit as a percentage of cost uses cost. Read which one is requested.
- A percentage-point difference and a percentage increase are different: 20% to 25% is 5 percentage points but a 25% relative increase.
Sources and review
SEAB 2026 syllabus: O-Level Mathematics 4052: percentage.
Original Rae practice, prepared with AI assistance. Selected numerical results and their displayed working are automatically checked at publication; this does not verify every explanation. Curriculum references checked on 5 September 2026. No teacher review or SEAB endorsement is claimed.
What the syllabus expects
- stating one quantity as a percentage of a second quantity
- using percentages to compare two quantities
- percentages that exceed 100%
- raising or lowering a quantity by a stated percentage
- working backwards from a percentage (reverse percentages)
Continue revising
- Ratio and proportion: sharing, scaling and inverse proportion
- Speed and rates: total distance, total time and unit conversions
- Probability: replacement, tree diagrams and checking outcomes
More O-Level Elementary Maths (E-Maths) topics
Whole numbers and the operations performed on them · Ratio and proportion · Rate and speed · Algebraic expressions and formulae · Functions together with their graphs · Equations and inequalities · all of O-Level Elementary Maths (E-Maths)