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Work backward from a percent: a mental math trick

When to use it: You know the amount after a percent change and want the amount before it.

Worked example

Working back from $96 after 20% offA bar for the original price, cut into tenths. $96 fills 80% of it, $12 a slice, so the whole bar is $120.original = ?original $120$12$12$12$12$12$12$12$12$12$12$96 is 80%20% is $24$120 − $24 = $96
  1. Say what share of the original you have: 20% off leaves 80%.
  2. Divide by that share, written as a decimal.
  3. Never add the percent back on. That uses the wrong base.

example After 20% off, a coat costs $96. What was the original price?

  1. $96 is 80% of the original.
  2. $96 ÷ 0.8 = $120.
  3. Check: 20% of $120 is $24, and $120 − $24 = $96.

Answer: $120

Try three

  1. After 40% off, a kettle costs $108. What was the original price?

    Show the answer

    $180

  2. After 10% off, a coat costs $72. What was the original price?

    Show the answer

    $80

  3. After 10% off, a lamp costs $216. What was the original price?

    Show the answer

    $240

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Used in: What percent? Work backward · Percentages in Business · Markup Is Not Margin

More mental math tricks

This technique and its worked example are Doing Math’s own lesson text, checked by a blind re-solve and a review on September 27, 2026.