Question

The retail price for a book was $30. It was marked down 20% on Black Friday. The next day, it was marked back up 30%. What was the percent increase on the original price?

Answer 1

We have a retail price that is marked down 20% one day and then marked up 30%.

The original price is P=30, so a marked down price P' will be:

$P^{\prime}=(1-0.2)\cdot P=0.8\cdot P=0.8\cdot30=24$

Then, if we mark up 30% this price will be:

$P^{\prime\prime}=(1+0.3)\cdot P^{\prime\prime}=1.3\cdot24=31.20$

Now we can compare the increase in price as:

$\begin{gathered} 1+i=\frac{P^{\prime\prime}}{P} \\ i=\frac{P^{\prime\prime}}{P}-1 \\ i=\frac{31.20}{30}-1 \\ i=1.04-1 \\ i=0.04 \\ i=4\% \end{gathered}$

Answer: the percent increase on the original price is 4%.