Rajlani sold a machine for Rs. 22000 with a discount of 8% on the labeled price and made a profit of $$22\frac{2}{3}$$% . What would have been the profit percent if the machine was sold without discount on the label price?

Solution(By Examveda Team)

Marked price of the machine = Rs. 22000
Selling price
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {22000 - \frac{{8 \times 22000}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. 20240}} \cr & {\text{Profit}} = 22\frac{2}{3}\% = \frac{{68}}{3}\% \cr} $$
Let cost price of the machine be Rs. x
$$\eqalign{ & \Rightarrow x + \frac{{68}}{3}\% {\text{ of }}x = {\text{Rs}}{\text{. }}20240 \cr & \Rightarrow x + \frac{{68x}}{{300}} = {\text{Rs}}{\text{. }}20240 \cr & \Rightarrow \frac{{368x}}{{300}} = {\text{Rs}}{\text{. }}20240 \cr & \Rightarrow x = {\text{Rs}}.\left( {\frac{{20240 \times 300}}{{368}}} \right) \cr & \Rightarrow x = {\text{Rs}}{\text{. }}16500 \cr} $$
Profit % when machine was sold without discount
$$\eqalign{ & = \frac{{22000 - 16500}}{{16500}} \times 100 \cr & = 33\frac{1}{3}\% \cr} $$