Kiran purchases an article for Rs. $$5310$$ which includes $$10$$% rebate on the marked price and $$18$$% tax (under GST) on the remaining price. Find the marked price of the article.
Given:
Rate of GST $$=18$$%
CP of an article $$=x-10$$% of $$x$$
$$=x-\dfrac{10}{100}x\\=\dfrac{90x}{100}\\=\dfrac{9x}{10}$$
Amount of GST on CP on article $$=18$$% of $$\dfrac {9x}{10$}$
$$=\dfrac {18}{100}\times \dfrac {9x}{10}$$
Total CP of article $$=\dfrac {9x}{10}+\left[\dfrac {18}{100}\times \dfrac {9x}{10}\right]\\=\dfrac{9x}{10}\left(\dfrac {1+18}{100}\right)=\dfrac {118}{100}\times \dfrac{9x}{10}$$
It is given that, CP of an article including tax $$=Rs.5310$$
So,
$$\dfrac {118}{100}\times \dfrac{9x}{10}=5310$$
$$\Rightarrow x=5310\times \dfrac {100}{118}\times \dfrac{10}9=5000$$
Hence, The required marked price of an article is Rs. $$5000$$