Question

After giving \[20\] percent discount, a saree is sold at $Rs.1120$. Find the marked price.

Answer 1

Hint: Discount is the difference of selling price and marked price. If discount percent is given, then that percent of marked price is calculated and subtracted from it to find the selling price. Alternatively, we can say that the selling price is $(100 - discount\% )\% $ of the marked price.

Formula used:
If selling price of an object is $SP$ and marked price is $MP$,
then discount is $MP - SP$
$ \Rightarrow discount\% = \dfrac{{MP - SP}}{{MP}} \times 100$
It is given $x\% $ discount on marked price means,
$SP = (100 - x)\% ofMP$
$ \Rightarrow SP = \dfrac{{(100 - x)}}{{100}} \times MP$

Complete step-by-step answer:
Given that after giving a $20$ percent discount, a saree is sold at $Rs.1120$.
We need to find the marked price of the saree. Let it be $MP$.
$20$ percent discount means the selling price of the saree is $(100 - 20) = 80\% $ of the marked price.
Let the selling price be $SP$. So we have $SP = 1120$
So we have $SP = 80\% MP$.
$ \Rightarrow SP = \dfrac{{80}}{{100}}MP$
Substituting the value for $SP$, we have
$ \Rightarrow 1120 = \dfrac{{80}}{{100}}MP$
Simplifying the Right Hand Side of the equation we get,
$ \Rightarrow 1120 = \dfrac{4}{5}MP$
Cross multiplying we get,
$MP = 1120 \times \dfrac{5}{4}$
Since $\dfrac{{1120}}{4} = 280$, we have,
$ \Rightarrow MP = 280 \times 5 = 1400$
Therefore, the market price of the saree is $Rs.1400$.

Additional information:
If more than one discount is given, the first discount is given on the marked price and second is applied on the resultant value and so on. Or we can simply calculate the effective discount using the formula of successive discounts.

Note: It is not necessary that selling price and marked price are different. They can be the same as well. In those cases the discount is said to be zero. If it is different, then marked price will be mentioned separately.