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 multiplies the original value
An increase of r% multiplies by 1+r; a decrease multiplies by 1−r, with r written as a decimal. Successive changes act on the newest value.
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
₱500 increased 20%: 500(1.20)=₱600.
₱800 discounted 25%: 800(0.75)=₱600.
₱660 after 10% increase: 660÷1.10=₱600.
20% then 10%: 0.80×0.90=0.72, an effective 28% discount.
20% off is cheaper than two successive 10% discounts because 0.80<0.81.
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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