After 20% off it costs $60, what was the original price?

Question

A common trap: adding 20% back to a sale price does not recover the original. Solve in your head. A jacket costs \60 after 20% off. What was the original price? Aim: under 10 seconds.

Accepted Answer

After 20% off you pay 80% of the original, so the sale price is 0.8 	imes 	ext{original}. Undo it by dividing: 	ext{original} = \frac{60}{0.8} = \frac{60 	imes 5}{4} = \frac{300}{4} = 75. So the original price was \mathbf{\75}. Check: 20\% of 75 is 15, and 75 - 15 = 60. Correct. Adding 20% to 60 would give 72, wrong, because that 20% is taken on the smaller base. Takeaway. To reverse a p\% discount, divide by (1 - p/100). Here divide by 0.8 (= multiply by 5/4). Never just add the percentage back.

After 20% off it costs $60, what was the original price?

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