Reverse Percent Problems
When the SAT gives you the result after a percent change and asks for the original, you divide — you don't reapply the percent.
Reading the concept isn't enough. The score comes from practicing the real Bluebook-style format and finding the exact mistakes you keep making.
What the SAT tests here
If a price after a $20\%$ discount is known, the result equals $0.8$ times the original. Solve for the original by dividing, using the multiplicative factor.
How to solve one, step by step
Example: after $20\%$ off, an item costs $\$48$. Original price?
- The sale price is $0.8$ of the original: $0.8x = 48$.
- Divide: $x = 60$, so $\$60$.
The mistakes that cost points
- Applying the percent to the result. Taking $20\%$ of $\$48$ answers a different question.
- Using an additive instead of multiplicative inverse. Reverse the multiplication by dividing by $0.8$, not by adding back $20\%$.
Practice questions
Try these the way you would on test day, then open the solution to check your method.
Easy
After a 25% increase, a number becomes 50. What was the original number?
- A$50$
- B$37.50$
- C$40$
- D$25$
Show solution
Answer: C, $40$. A 25% increase means the result equals $1.25$ times the original. Set up $1.25x = 50$ and divide both sides by $1.25$: $x = \frac{50}{1.25} = 40$.
Medium
A town's population decreased by 12% and now stands at 17,600. What was the population before the decrease?
- A$19{,}712$
- B$15{,}488$
- C$20{,}000$
- D$17{,}600$
Show solution
Answer: C, $20{,}000$. A 12% decrease means current population $= 0.88 \times \text{original}$. Set up $0.88x = 17{,}600$ and divide: $x = \frac{17{,}600}{0.88} = 20{,}000$.
Hard
After a 35% markup, a wholesale item sells for $\$270$. A buyer wants to know the wholesale cost. What was the wholesale cost?
- A$\$175.50$
- B$\$200$
- C$\$135$
- D$\$270$
Show solution
Answer: B, $\$200$. A 35% markup means selling price $= 1.35 \times \text{cost}$. Set up $1.35x = 270$ and divide: $x = \frac{270}{1.35} = 200$.
Find your exact gaps
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