Question:
After allowing a discount of 10% on the marked price, a trader still makes a gain of 17%. By what per cent is the marked price above the cost price?
Solution:
Let $R s 100$ be the cost price.
Gain required = $17 \%$
$\therefore$ Selling price $=R s 117$
Let the marked price be $R s x$.
Then, discount $=10 \%$ of $\mathrm{x}$
$=\frac{10}{100} \times x$
$=\frac{x}{10}$
Selling Price = MP − discount
$\Rightarrow 117=x-\frac{x}{10}$
$\Rightarrow 117=\frac{9 x}{10}$
$\Rightarrow 9 x=1170$
$\Rightarrow x=\frac{1170}{9}$
$\Rightarrow x=130$
$\therefore$ Marked price $=R s 130$
Hence, the marked price is $30 \%$ above the cost price.