A shopkeeper sells 25 articles at Rs. 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, the profit gained is = ?

Selling price of 1 article = Rs. 45
Let marked price of each article be Rs. x
Then,
$$\eqalign{ & \frac{{90}}{{100}}x = 45 \cr & x = {\text{Rs}}{\text{.}}\left( {\frac{{45 \times 100}}{{90}}} \right) \cr & \,\,\,\,\,\, = {\text{Rs}}{\text{. 50}} \cr & {\text{CP}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{150}} \times 45} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 30}} \cr} $$
When no discount is given,
Cost price = Rs. 30,
Selling price = Rs. 50
∴ Required profit %
$$\eqalign{ & = \left( {\frac{{20}}{{30}} \times 100} \right)\% \cr & = 66\frac{2}{3}\% \cr} $$