Question

If S.P. of Rs.$24$ results in a $20\% $ discount on list price, what S.P. would result in a $30\% $ discount on list price?
A) Rs.$18$
B) Rs.$20$
C) Rs.$21$
D) Rs.$27$

Answer 1

Hint: First find the selling price for the $20% $ discount on list price assuming the list price to be $100$ using the formula S.P.=${\text{List price - discount}}$. Then find the list price for selling price Rs. $24$. With this list price we can find the discount of $30% $ on list price. Then again use the given formula to find S.P.

Complete step-by-step answer:
Given, there is $20% $ discount on list price.
So let us assume the list price is Rs.$100$ then using the formula - S.P. =${\text{List price - discount}}$, we can find the S.P.
On putting the given values, we get
$ \Rightarrow $ S.P. =$100 - 20$
On subtraction, we get
$ \Rightarrow $ S.P.$ = 80Rs.$
This means for S.P. of Rs.$80$, the list price is Rs.$100$
Then for S.P. Rs.$1$, list price is $ = \dfrac{{100}}{{80}}$
  So I f S.P. is Rs. $24$then the list price will be $ = \dfrac{{100}}{{80}} \times 24$
On solving, we get
List price=$ = \dfrac{{100}}{{80}} \times 24 = 10 \times 3$
List price $ = {\text{Rs}}.30$
Now we have to find $30\% $ discount on list price,
We already know that list price so,
$30\% $ of $30 = \dfrac{{30}}{{100}} \times 30$
On solving the equation, we get
$30\% $ of $30 = 3 \times 3 = 9$
So discount=$9$ Rs.
We have to find the S.P. which results in $30\% $ discount on list price. We know the formula,
S.P. =${\text{List price - discount}}$
On substituting the given values we get-
S.P. =$30 - 9 = 21$ Rs.
Hence, for S.P. of Rs.$21$ there is $30\% $ discount on list price.
So the answer is ‘C’.

Note: List price is also known as Marked Price. Discount is only offered when the marked price of the product is greater than the selling price of the product. It is given to attract the customers by the shopkeepers to make more sales. You can also use the formula-
$ \Rightarrow {\text{SP = M}}{\text{.P}}{\text{. - }}\dfrac{{{\text{M}}{\text{.P}}{{. \times Discount\% }}}}{{100}}$ to find S.P.
On putting the given values in the formula we get,
$\
   \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 30 - \dfrac{{30 \times 30}}{{100}} = 30 - \left( {3 \times 3} \right) \\
   \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 30 - 9 = 21 \\
 $
So using this formula we can find the value of S.P.=$21$ Rs.