Question

A sofa regularly sells for $ \$ 790$. The sale price is $ \$624.10$. How do you find the percent decrease of the sale price from the regular price? \[\]

Answer 1

Hint: We recall regular price and sales price what type of changes that go into increasing or decreasing the price. We take the regular price $\left( \text{RP} \right)$ as the original amount, the sales price $\left( SP \right)$ as changed amount and find the change as $D=RP-SP$ if $RP>SP$ and $D=SP-RP$ if $SP>DP$. We find the percentage change as $\%D=\dfrac{D}{RP}\times 100$.\[\]

Complete answer:
We know that the regular price $\left( RP \right)$ is the price at which the good or service originally was meant to be sold. Then the price may decrease because of discounts, festival offers or may increase taxes or additional services like transportation. The seller takes care of his/her profit and the price after the change at which he sells it to the customer is called sales prices.\[\]
The change in regular price and sales price is the change is the in amount which is given by
\[D=\left\{ \begin{matrix}
   RP-SP & \text{if }RP > SP \\
   SP-RP & \text{if }SP > RP \\
\end{matrix} \right.\]
The percentage change is calculated on the initial or original price which here is regular price as
\[\%D=\dfrac{D}{RP}\times 100\]
We are given the question that A sofa regularly sells for $\$790.$ The sale price is $\$624.10.$ So regular price is $RP=\$720$ and sales price is $SP=\$624.10$. Since sales price is smaller there is a decrease in price which in amount is
\[D=RP-SP=\$720-\$624.10= $165.90\]
The percentage change is percentage decrease in price as
\[\%D=\dfrac{165.90}{790}\times 100=\dfrac{16590}{790}=21\]

Note: We note that if the original amount is ${{x}_{o}}$ and change amount is ${{x}_{c}}$ then percentage change is given by $\dfrac{\left| {{x}_{c}}-{{x}_{o}} \right|}{{{x}_{o}}}\times 100$. The change in prices may also happen over years or months because of increases in supply or demand. The decrease in price over a time period is called depreciation and increase is called appreciation. This type change is calculated using simple interest or compound interest formula.