Question 1

How do I find the original price before a percentage increase?

Accepted Answer

Divide the current price by (1 + rate). If the price increased by 15% and is now $115: Original = 115 / 1.15 = $100. The multiplier 1.15 represents 100% + 15% = 115% of the original. Dividing reverses this multiplication. Common mistake: subtracting 15% from $115 gives $97.75, not $100 — that is wrong because 15% of $115 ≠ 15% of $100.

Question 2

How do I find the original price before a percentage decrease?

Accepted Answer

Divide the current price by (1 − rate). If the price decreased by 30% and is now $70: Original = 70 / (1 − 0.30) = 70 / 0.70 = $100. Common mistake: adding 30% to $70 gives $91, not $100. This error occurs because 30% of $70 ≠ 30% of $100.

Question 3

What does "X is Y% of what number?" mean?

Accepted Answer

This phrase asks you to find the whole when you know a part and the percentage. "30 is 60% of what number?" means: 30 = 0.60 × Original → Original = 30 / 0.60 = 50. The formula is simply: Original = X / (Y/100), or equivalently Original = X × (100/Y).

Question 4

How do I reverse a VAT / sales tax calculation?

Accepted Answer

To find the pre-tax price from the total: Pre-tax = Total / (1 + TaxRate/100). Example with 20% VAT: Pre-tax = 120 / 1.20 = $100. With 8.5% sales tax: Pre-tax = 108.50 / 1.085 = $100. Always divide by (1 + rate), not subtract the tax amount — subtracting gives the wrong base.

Question 5

What if the percentage applied was compound (multiple steps)?

Accepted Answer

Apply the reversal in reverse order. If 10% was added then 20% was added: Original = Final / (1.10 × 1.20) = Final / 1.32. If 10% was added then 15% was removed: Original = Final / (1.10 × 0.85) = Final / 0.935. The key is to multiply all the factors together, then divide the final value by that product.

Question 6

Why can't I just subtract or add back the percentage directly?

Accepted Answer

Because the percentage is always taken of the original, not the result. A 25% increase on $100 gives $125. Subtracting 25% of $125 gives $125 − $31.25 = $93.75 — not $100. This is the most common reversal error. Always use division: $125 / 1.25 = $100 exactly.

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Reverse Percentage Calculator

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