A shopkeeper sold an item for Rs. 1510 after giving a discount of $$24\frac{1}{2}\% $$   and there by incurred a loss of 10%. Had he sold the item without discount his net profit would have been = ?

Solution(By Examveda Team)

Let the marked price of an item = Rs. x
Selling price of an item $$ = \left( {100 - 24\frac{1}{2}} \right)\% \,{\text{of }}x$$
$$\eqalign{ & \Rightarrow 1510 = \frac{{151}}{2} \times \frac{1}{{100}} \times x \cr & \Rightarrow x = {\text{Rs}}{\text{. 2000}} \cr & {\text{Cost price of an item }} \cr & = 1510 \times \frac{{100}}{{90}} \cr & {\text{ = Rs}}{\text{. }}\frac{{15100}}{9} \cr & {\text{Without discount, gain}} \cr & {\text{ = }}2000 - \frac{{15100}}{9} \cr & = \frac{{18000 - 15100}}{9} \cr & = \frac{{2900}}{9} \cr & = {\text{Rs}}{\text{. 322}}\frac{2}{9} \cr} $$