Working backwards

$80 after 20% off? It wasn’t $96.

"MRR grew 25% to $50k. What was it last month?" Most people add 25% back on and get it wrong. Getting this right is how you catch errors in board decks.

The move

Turn the percent into a multiplier: +25% means × 1.25, −20% means × 0.8. To go backwards, divide by that multiplier.

Worked example

After a 20% discount a plan costs $80. Original price?

  1. −20% means you pay 80% → × 0.8
  2. original × 0.8 = $80
  3. original = 80 ÷ 0.8 = $100
  4. Check: 20% of $100 is $20, and $100 − $20 = $80 ✓
  • Adding the 20% back on ($80 + $16 = $96) is the trap. The 20% was taken off the *original*, not the discounted price.
  • Dividing by 0.8 is the same as × 10 ÷ 8, or × 5 ÷ 4.