Know the result and the percentage? Work backwards to the original number.
Original Value
1,000
Sometimes you know the result of a percentage calculation but not the number it started from — for example, you see a discounted price and want to know what the item cost before the discount. This is a reverse percentage problem, and it needs a slightly different formula to the usual "find X% of Y."
The key idea is that after a percentage change, the final value represents (100% ± the percentage) of the original — so dividing back by that adjusted percentage gets you to the original number.
Formula
Original Value = Final Value ÷ (1 ± (Percentage ÷ 100))
Use minus for a discount/decrease, plus for a markup/increase, in the denominator.
Worked Example
Worked example
The mistake almost everyone makes
A very common error is adding 20% of ₹800 back on (₹800 + ₹160 = ₹960) — but that is wrong, because 20% of the ORIGINAL price is not the same as 20% of the discounted price. Reverse percentage must divide, not multiply, to correct for this.
Works for increases too
The same logic applies to markups and price increases — if a price of ₹1,150 already includes a 15% increase, the original was ₹1,150 ÷ 1.15 = ₹1,000. Just use "+ " instead of "−" in the formula for anything that went up rather than down.
Frequently Asked Questions
How do I find the original price before a discount?
Divide the sale price by (1 − discount as a decimal). For a 25% discount resulting in ₹750, that is ₹750 ÷ 0.75 = ₹1,000.
Why can't I just add the percentage back to the discounted price?
Because the percentage was originally calculated on the higher, original price — not on the smaller, discounted price. Adding it back on the discounted amount always gives too small a number.
Does this work for price increases too?
Yes — use the same formula but add the percentage instead of subtracting it: Original = Final ÷ (1 + percentage/100).
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