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.$27$

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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.

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.
$\Rightarrow {\text{SP = M}}{\text{.P}}{\text{. - }}\dfrac{{{\text{M}}{\text{.P}}{{. \times Discount\% }}}}{{100}}$ to find S.P.
$\ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 30 - \dfrac{{30 \times 30}}{{100}} = 30 - \left( {3 \times 3} \right) \\ \Rightarrow {\text{S}}{\text{.P}}{\text{.}} = 30 - 9 = 21 \\$
So using this formula we can find the value of S.P.=$21$ Rs.