To find the original value before a percentage change, write the final value as a decimal multiple of the original, then divide the final value by that multiplier. A price after a 20% discount is 80% (0.8) of the original, so original = final ÷ 0.8, never final + 20%. The same divide-back rule works for increases: a price after 9% GST is 109% (1.09) of the pre-GST price.
Reverse percentage questions give you the value after a percentage increase or decrease and ask for the value before it. The instinctive move is to undo the percentage by adding or subtracting it from the final value. That instinct is wrong, because the percentage was calculated on the original value, not on the final value.
Take a shirt discounted by 20% to $64. Adding 20% of $64 back gives $64 + $12.80 = $76.80. That is not the original price. The 20% discount was taken off the original price, not off $64, so working backwards from $64 by a straight percentage add-back always lands on the wrong number. This is the reverse of a profit and loss question, which starts from the original cost price and works forward to a selling price instead.
Step 1
Write the final value as a % of the original
Step 2
Convert that % to a decimal multiplier
Step 3
original = final ÷ multiplier
Step 4
Check: multiply your answer by the multiplier
A jacket is sold at a 20% discount. The sale price is $64. Find the original price.
Solution
80% = 0.8.original = 64 ÷ 0.8 = 80.Quick check: apply the 20% discount to $80. A 20% discount off $80 is $80 × 0.8 = $64, which matches the sale price given in the question. This confirms the answer.
A laptop bag costs $218.00 after 9% GST is added. Find the price before GST.
Solution
109% = 1.09.pre-GST price = 218 ÷ 1.09 = 200.Quick check: add 9% GST to $200. $200 × 1.09 = $218, which matches the GST-inclusive price given in the question. This confirms the answer.
The step students get wrong
Adding or subtracting the percentage from the final value instead of dividing. A 20% discount does not mean you add 20% of the sale price back on, and a 9% GST increase does not mean you subtract 9% of the GST-inclusive price. The percentage change was always calculated on the original value, so the only way back to the original is to identify what percentage the final value represents and then divide by that decimal multiplier.
How do I know whether to use a multiplier above 1 or below 1?
A decrease (discount, depreciation, loss) gives a multiplier below 1, found from 100% minus the percentage change. An increase (GST, mark-up, interest) gives a multiplier above 1, found from 100% plus the percentage change. Identify whether the value went up or down before you build the multiplier.
Can I use this method for percentage increase questions too, not just GST?
Yes. Any question that gives you a value after a percentage increase and asks for the value before it uses the same divide-back method: write the final value as (100 + increase)% of the original, convert to a decimal multiplier, then divide.
What if the question gives two percentage changes applied one after another?
Work backwards one step at a time, undoing the most recent change first. Divide by the multiplier for the second change to reverse it, then divide the result by the multiplier for the first change. Do not combine the two percentages into one before dividing.
Is this the same idea as simple and compound interest?
Reverse percentage and interest calculations both use a decimal multiplier, but they run in opposite directions: interest questions usually ask you to find the final amount from the original, while reverse percentage questions give you the final amount and ask for the original. See our guide on simple interest versus compound interest for how the multiplier is built when you are working forwards.
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