A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10% . If he gains Rs. 56 on one item, his advertised price of the item, in Rs. is = ?

Solution(By Examveda Team)

Advertised price of the item = N
∴ Commission on advertised price of the article = $$\frac{{N \times 23}}{{100}}$$
Price after commission = $$N - \frac{{23N}}{{100}} = \frac{{77N}}{{100}}$$
$$\eqalign{ & \therefore {\text{CP}}\,{\text{of}}\,{\text{the}}\,{\text{item}} \cr & \frac{{\frac{{77N}}{{100}} \times 100}}{{100 + 10}} \cr & = \frac{{77N}}{{110}} \cr & = \frac{{7N}}{{10}} \cr & {\text{Profit}} = \frac{{77N}}{{110}} - \frac{{7N}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{7N}}{{110}} \cr & \Rightarrow 56 = \frac{{7N}}{{110}} \cr & \therefore N = \frac{{56 \times 100}}{7} = 800 \cr} $$