Aditya, a trader, sells an item to a retailer at 20% discount, but charges 10% on the discounted price, for delivery and packaging. The retailer sells it for Rs. 2046 more, thereby earning a profit of 25%. At what price had the trader marked the item ?

Solution(By Examveda Team)

Let the marked price of the item be Rs. 100x
Discount % = 20%
Changes for delivery and packaging
= 10% on discounted price
Then,
\[100x\xrightarrow{{ - 20\% }}80x\xrightarrow{{ + 10\% }}88x\]
$$\eqalign{ & \therefore 88x + 88x \times \frac{{25}}{{100}} - 88x = 2046 \cr & \Rightarrow 110x - 88x = 2046 \cr & \Rightarrow 22x = 2046 \cr & \Rightarrow x = 93 \cr & {\text{Hence,}} \cr & 100x = 39 \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 9300 \cr & \therefore {\text{Marked price}} = {\text{Rs}}{\text{.}}\,{\text{9300}} \cr} $$