Question

The price of a painting in an art gallery was decreased by $20\%$. If the price is again increased by $20\%$, then the final price will be ___________ the original price.

• A. Cannot be determined from the given data
• B. more than
• C. less than
• D. equal to

Answer 1

The correct option is C less than

Let $\$100$ be the original price of the painting.
New price after 20% decrease $=(100-20)\%\text{of}100$
$=\frac{80}{100}\times 100=\$80$

New price after $20\%$ increase $=(100+20)\%\text{of}80$
$=\frac{120}{100}\times 80=\$96$

Since the new price of $\$96$ is less than $\$100$, the final price is less than the original one.
Thus, the final price will be less than the original price.