Question

If a shirt costs \$30 after a 20% discount, what was the original price?

• A. \$36
• B. \$37.50
• C. \$38
• D. \$40

Hint:

A common mistake is to add 20% of \$30 to \$30. Remember that the discount was calculated on the original, higher price. To reverse a percentage decrease, you must divide by the remaining percentage.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a reverse percentage problem. We are given the final price after a discount and need to find the original price.
Step 2: Key Formula or Approach:
Let \(P\) be the original price.
Final Price = Original Price \(\times\) (1 - Discount Rate)
We need to solve for \(P\).
Step 3: Detailed Explanation:
The discount is 20%, or 0.20.
The discounted price is \$30.
If a 20% discount was applied, the final price represents \(100% - 20% = 80%\) of the original price.
So, \$30 is 80% of the original price \(P\).
\[ 30 = 0.80 \times P \] To find \(P\), divide \$30 by 0.80:
\[ P = \frac{30}{0.80} = \frac{30}{4/5} = 30 \times \frac{5}{4} = \frac{150}{4} \] \[ P = 37.50 \] The original price was \$37.50.
Step 4: Final Answer:
The original price of the shirt was \$37.50. This corresponds to option (B).