Question

The original price of a hat was $36.00$ and the marked price is $27.00$. Lisa bought the hat at a marked price. What percent of the price has the hat been marked down?

Answer 1

Hint:In this question, we have given the original price and the marked price of the hat and we have to find out the percentage of the original price that has marked down. Marked price is the price which is written on the product and the original price is the original value of that product.

Formula Used:
(Marked down price ÷ Original price)$ \times 100\% $

Complete step by step answer:
Let us consider the original price as OP, the marked price as MP and the marked down price as x. So,
$OP = 36$, $MP = 27$
Firstly, we have to find the price that has marked down and to find this, we need to subtract the marked price from the original price. The marked down price is
$x = OP - MP \\
\Rightarrow x = 36 - 27 \\
\Rightarrow x = 9 \\ $
Hence,$9$ is the price that has been marked down. Now, we have to find the percentage of the price of the hat that has been marked down. To find this, we need to divide the marked down price by the original price and then multiply it with $100\% $.
(Marked down price ÷ Original price)$ \times 100\% $
$\dfrac{x}{{OP}} \times 100\% $
Now, we will substitute the values into this formula.
$\dfrac{x}{{OP}} \times 100\% = \dfrac{9}{{36}} \times 100\% \\
\Rightarrow\dfrac{x}{{OP}} \times 100\% = \dfrac{1}{4} \times 100\% \\
\therefore\dfrac{x}{{OP}} \times 100\% = 25\% \\ $
Hence, $25\% $ of the original price is the price of what has been marked down.

Note:The original price of the hat is $36.00$ and $25$ percent of the original price is the price of hat being marked down. Now, we can also find the marked price of the hat. The marked price will be the difference of the original price and $25\% $ of the original price.
$MP = OP -25\% $ of OP
$= 36 - \left( {\dfrac{{25}}{{100}} \times 36} \right) \\
\Rightarrow MP= 36 - 9 \\
\Rightarrow MP= 27 $
And, $27$ is the marked price of the hat.