To find the original price after two successive percentage discounts, divide the final price by the multiplier for each discount. If an item is reduced by 20% and then by a further 10%, the customer pays 0.80 × 0.90 = 0.72 of the original price.
The 2027 SEC G2 Mathematics K210 syllabus includes percentage changes and reverse percentages. This example uses a second discount calculated on the sale price, then compares it with a voucher that takes off a fixed dollar amount.
- Identify the price on which each discount is calculated.
- Convert each percentage discount into a multiplier.
- Divide by the multipliers to work backwards.
- Apply both discounts forwards to verify the result.
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Give each percentage a price
The first discount of 20% is calculated on the original price. After it is applied, the amount left is 80% of that price. The further 10% is calculated on the reduced price. After it is applied, the amount left is 90% of the reduced price.
A quick check uses an imaginary original price of $100. The first reduction leaves $80. The second takes 10% of $80, or $8, so the final price is $72. The overall discount is 28% of the original price.
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Worked example | The final receipt shows $54
A bag is marked down by 20%. A membership discount then takes a further 10% off the reduced price. A customer pays $54. Work backwards from the receipt. Before the membership discount, the price was $54 ÷ 0.90 = $60. Before the first discount, it was $60 ÷ 0.80 = $75.
You can combine both steps by writing $54 ÷ 0.72 = $75. Check forwards from $75. The first discount removes $15 and leaves $60. The second removes $6 and leaves $54. The customer saved $21, which is 28% of $75.
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Change the second discount to a fixed amount
Suppose the second offer is now a $10 voucher applied after the 20% discount, and the final price is again $54. Restore the $10 first to get $64. The sale price of $64 is 80% of the original, so the original price was $64 ÷ 0.80 = $80.
Forward check: $80 × 0.80 − $10 = $54. In this version the voucher always subtracts $10. In the first version the membership discount takes an amount that depends on the price at that step.
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Try a pair of prices that look similar
A jacket costs $72 after two successive discounts of 25% and 20%. Before doing the arithmetic, decide what share of the original price remains. The share is 0.75 × 0.80 = 0.60, so the original price is $72 ÷ 0.60 = $120.
Compare that result with a single 45% discount. A final price of $72 would then be 55% of the original, giving about $130.91. Read whether the problem describes a single discount or one discount followed by another before choosing the calculation.
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Frequently asked questions
Why divide by 0.90 instead of adding 10%?
The original 10% was calculated on the higher price before that discount. Dividing the final price by 0.90 recovers the price that was treated as 100%.
Can I reverse two ordinary percentage discounts in either order?
The product of the two multipliers stays the same if you swap them. Reverse the stated order when you need the intermediate price or when a fixed voucher or a discount condition changes the calculation.
What should a parent ask when the answer looks plausible?
Ask the student to apply both discounts to their answer and reproduce the amount paid. Ask them to name which price each percentage uses.
Sources and next reading
Read the official SEAB syllabus
When the leading coefficient is zero in G2 Additional Mathematics