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 = ?

Answer: Option D

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