Question

A store is having a sale where winter clothes are \[60\% \] of the original price. A sweater is on sale for \[30\$\]. What was the original price of the sweater?

Answer 1

Hint: In the above problem, we are given the cost of a sweater after a 60% discount to be $30\$$. We need to find the original price of the sweater. There is a 60% discount on all the winter clothes, that means the store is selling winter clothes at only 100-60 i.e, 40% of the original cost. Now given that the sweater is being sold for $30\$$, that means the selling price of the sweater is 40% of its original cost. Therefore by knowing the 40% cost, we can easily calculate the 100% cost i.e. the original cost by doing some small calculations.

Complete step by step answer:
We are given that, the discount percentage on all winter clothes is
\[ \Rightarrow 60\% \]
Also the sweater is on sale for \[30\$ \] , so we can write
The marked price after the \[60\% \] discount of the sweater is
\[ \Rightarrow 30\$ \]
We need to find the original price of the sweater.
Since, there is \[60\% \] discount on all the winter clothes,
Therefore, we can write that the store is selling winter clothes at only
\[ \Rightarrow \left( {100 - 60} \right)\% \]
That is, at only
\[ \Rightarrow 40\% \]
 of the original cost.
So, the sweater is being sold at only \[40\% \] of its original cost. But the sweater is being sold at a price of \[30\$ \]. That means, \[40\% \] of the original price is equal to \[30\$ \] .

Let the original price of the sweater be \[x\]. Therefore, we can write \[40\% \] of \[x\] is equal to \[30\$ \]. That gives,
\[ \Rightarrow \dfrac{{40}}{{100}} \times x = 30\$ \]
Or we can write it as,
\[ \Rightarrow \dfrac{4}{{10}} \times x = 30\$ \]
Multiplying both sides by \[\dfrac{{10}}{4}\] , we get
\[ \Rightarrow \dfrac{4}{{10}} \times \dfrac{{10}}{4} \times x = 30\$ \times \dfrac{{10}}{4}\]
On solving we get,
\[ \Rightarrow x = \dfrac{{300}}{4}\$ \]
Therefore,
\[ \therefore x = 75\$ \]
That is the required original price.

Therefore, the original price of the sweater is \[75\$ \].

Note: In such problems, based on percentage the original price at which a product is purchased by the store or individual is called the cost price or CP of that product. The new price at which the product is sold to others is called the selling price or SP. Also, if there is a discount marked on a product, then the new price of the product is called the marked price or MP. When MP or SP are greater than the CP, then it is said to be a profit. Otherwise, if MP or SP are less than the CP, then it is said to be a loss. Profit or loss is equal to the difference between CP and SP or MP. The profit/loss percentage is given by,
\[ \Rightarrow profit/loss\% = \dfrac{{profit/loss}}{{CP}} \times 100\] .