Question

If $1,500$ is increased by $20\%$ and then reduced by $y\%$, yielding $1,080$, what is $y$ ?

• A. $40$
• B. $60$
• C. $20$
• D. $45$

Answer 1

Answer: (A)

The correct option is A $40$
Break the question into two parts.
First, $1,500$ is increased by $20\%$. Thus, $120\%$ percent of $1,500$ is:
$\left(\frac{120}{100}\right)1500=1800$
$\Rightarrow \left(\frac{6}{5}\right)1500=1800$
$\Rightarrow \left(6\right)300=1800$
You are solving for $y$, which represents the percent change of $1,800$:
Percent Change $=$ Change in Value/Original Value
The change in value from $1,800$ to $1,080$ is $1,800-1,080=720$
$\Rightarrow \frac{x}{100}=\frac{720}{1800}$
You can save time by noticing that $720$ and $1,800$ are both divisible by $360$:
$\Rightarrow \frac{y}{100}=\frac{2}{5}$
$\Rightarrow y=\frac{200}{5}=40$