Question

A jacket is on sale for \[20\% \] off the regular price. The sale price is \[\$ 50\]. What is the regular price of the jacket?

Answer 1

Hint: Here, a jacket is on sale for \[20\% \] off the regular price i.e., discount percentage is given. We will assume the regular price of the jacket to be \[x\]. Then we will calculate \[20\% \] of \[x\] to find the amount of discount. Selling price is given in the question as \[\$ 50\]. As we know, selling price \[ = \] regular price \[ - \] discount, using this we will calculate the regular price of the jacket.

Complete step by step answer:
Given, a jacket is on sale for \[20\% \] off the regular price. In other words, a discount of \[20\% \] is given on the regular price of the jacket.
Also, given that the selling price is \[\$ 50\].
Let the regular price of the jacket be \[x\].
To calculate the regular price, we have to first calculate what is \[20\% \] off the regular price i.e., \[ \Rightarrow 20\% {\text{ of }}x = \dfrac{{20}}{{100}} \times x\]
\[ = \dfrac{x}{5}\]
Therefore, selling price \[ = \] regular price \[ - \] discount
\[ \Rightarrow {\text{selling price}} = x - \dfrac{x}{5}\]
Since, the sale price is \[\$ 50\]. So, on equating we get
\[ \Rightarrow 50 = x - \dfrac{x}{5}\]
On taking the LCM of right hand side, we get
\[ \Rightarrow 50 = \dfrac{{5x - x}}{5}\]
\[ \Rightarrow 50 = \dfrac{{4x}}{5}\]
On cross multiplication, we get
\[ \Rightarrow 4x = 50 \times 5\]
\[ \Rightarrow 4x = 250\]
Dividing both the sides by \[4\], we get
\[ \Rightarrow x = \dfrac{{250}}{4}\]
On calculation, we get
\[ \Rightarrow x = 62.5\]
Therefore, the regular price of the jacket is \[\$ 62.50\].

Note:
Percentage is a number or ratio expressed as a fraction of \[100\]. It is often denoted by percent sign i.e., \['\% '\]. A percentage is a dimensionless number and it has no unit of measurement. They are often used to express a proportionate part of a total or a relative value indicating hundredth parts of any quantity.