Question

After allowing the discount of $10\% $ on the marked price a trader still makes the gain of $17\% $. What percent is the marked price above the cost price?

Answer 1

Hint: let us assume that the cost price be ${\text{Rs 100}}$ and the marked price be${\text{Rs }}x$. Now we have $10\% $ discount on the marked price that means that the selling price will be $x - \dfrac{{10x}}{{100}} = \dfrac{{9x}}{{10}}$
Now we need to find the gain percent.
Gain percent$ = \dfrac{{{\text{selling price}} - {\text{cost price}}}}{{{\text{cost price}}}} \times 100\% $
Here we can denote the selling price by $SP$ and the cost price by $CP$

Complete step-by-step answer:
Here we are said that after allowing the $10\% $ discount on the marked price and the trader still makes the gain of $17\% $ and that means that the trader purchase the product for the same money and then he increase the money of the product and then gives $10\% $ discount and he gains the $17\% $ from the product and we need to find the gain percent of the percent increase of the marked price from the cost price. So let us assume that the trader initially purchase the product for ${\text{Rs 100}}$
Now let us assume that marked price of the product be ${\text{Rs }}x$
So here we assumed that
Cost price$ = {\text{Rs 100}}$
Marked price$ = {\text{Rs }}x$
We know that he gains $17\% $ after giving the discount of $10\% $ on the marked price
So the selling price would become $ = x - 10\% {\text{ of }}x$
Here $10\% {\text{ of }}x$ is the discount provided
So the $SP = x - \dfrac{{10x}}{{100}} = \dfrac{{100x - 10x}}{{100}} = \dfrac{{90x}}{{100}} = \dfrac{{9x}}{{10}}$
So we got that $SP = \dfrac{{9x}}{{10}}$
Now as it is given that gain percent is $17\% $ and we know that the
Gain percent$ = \dfrac{{{\text{selling price}} - {\text{cost price}}}}{{{\text{cost price}}}} \times 100\% $
We know that
$SP = \dfrac{{9x}}{{10}}$,$CP = 100$
So we get that
$
\Rightarrow {\text{gain percent}} = \dfrac{{\dfrac{{9x}}{{10}} - 100}}{{100}} \times 100 \\
\Rightarrow 17 = \dfrac{{\dfrac{{9x}}{{10}} - 100}}{{100}} \times 100 \\
\Rightarrow 17 = \dfrac{{9 x}}{{10}} - 100 \\
\Rightarrow \dfrac{{9x}}{{10}} = 117 \\
\Rightarrow x = \dfrac{{1170}}{9} = 130 \\
 $
Hence we get that $CP = 100$
Marked price $ = 130 - 100 = {\text{Rs 30 more than the CP}}$
We can say therefore that ${\text{marked price}} = 100 + 30 = {\text{Rs 130}}$
So the percent increase$ = \dfrac{{130 - 100}}{{100}} \times 100 = 30\% $

Note: If we are given the cost price and the selling price then the gain percent is given by the formula
Gain percent$ = \dfrac{{{\text{selling price}} - {\text{cost price}}}}{{{\text{cost price}}}} \times 100\% $
If we need to find the lose percent then it is given by$ = \dfrac{{{\text{cost price}} - {\text{selling price}}}}{{{\text{cost price}}}} \times 100\% $
So for the profit, $SP > CP$
And for the loss, $CP > SP$