How to calculate reverse percentages without a calculator?

Mastering Reverse Percentages in Your Head

Ever seen a sign advertising 20% off with a final price tag of $80, and wondered what the original price was? Finding the starting amount before a price drop or increase is called calculating reverse percentages, and you do not need a calculator to pull it off.

The secret lies in working backward from the percentage you actually have, rather than the one you lost or gained. Start by finding out what percentage the current amount represents relative to the original 100%. If an item is discounted by 20%, your current price equals 80% of the original value. If an item increased in value by 10%, your current total represents 110%.

Once you know that baseline percentage, use a simple two-step mental math trick to reach the initial total:

First, calculate what 1% is worth. To do this, take your current amount and divide it by the percentage you identified in the previous step. For example, if $80 represents 80%, divide 80 by 80 to learn that 1% is equal to $1.

Second, scale back up to the full original value. Multiply your 1% figure by 100 to find the 100% total. Since $1 multiplied by 100 is $100, your original price was $100.

This straightforward strategy works for both discounts and price hikes. By breaking the problem down to find 1% first, you can quickly untangle sale prices, tax additions, and interest rates entirely in your head.