Percent Change and Successive Discounts
Use multipliers to compare changes quickly and avoid adding successive percentages.
Percent Change and Successive Discounts
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Percent change acts on a base amount
Convert each percent change into a multiplier. An increase of r% uses 1+r; a decrease uses 1−r, with r written as a decimal. For successive changes, multiply the factors in the order they occur. To recover an original amount, divide the final amount by the combined multiplier.
New value
new = original × multiplier
Original value
original = new ÷ multiplier
See the multiplier shortcut in a real discount
Problem: A ₱1,000 bag is discounted by 20%, then by another 10%. What is the final price?
Recognize: Each discount acts on the price left after the previous discount.
Do it fast: 20% off means keep 80%, or ×0.80. Then 10% off means keep 90%, or ×0.90.
₱1,000 × 0.80 × 0.90 = ₱720.
The overall discount is ₱280, or 28%—not 30%.
Why it works
The second 10% is taken from ₱800, not from the original ₱1,000. That is why successive percentages must be multiplied.
Five forms you should recognize
A ₱750 fee increases by 12%.
₱750(1.12)=₱840A ₱1,600 item is 25% off, so the customer pays 75%.
₱1,600(0.75)=₱1,200Twenty percent off followed by 10% off leaves:
0.80(0.90)=0.72The customer pays 72%, so the effective discount is 28%—not 30%.
A fee becomes ₱920 after a 15% increase.
original=₱9201.15=₱800A 20% increase followed by a 20% decrease gives:
1.20(0.80)=0.96The final value is 4% below the original because the two percentages use different bases.
Check before you commit
- Adding successive discounts
- Using the percent as the final multiplier
- Subtracting a percent from pesos
- Multiplying backward when finding the original
- Assuming equal increase and decrease cancel
- Rounding too early
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Percent Change and Successive Discounts FAQ
Why are there two mastery sets?
A different five-question set appears after an unsuccessful attempt so memorizing one set does not verify mastery.
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