A shopkeeper allows a discount of 10% to his customer and still gain 20%. Find the marked price of an article which cost rupees 450 to the shopkeeper.

Given: 

A shopkeeper allows a discount of 10% to his customer and still gain 20%.

To do: 

We have to find the marked price of an article which cost rupees 450 to the shopkeeper.

Solution:

Cost price $= Rs.\ 450$

Profit $ \% = 20 \%$

Profit $= \frac{Profit \% \times CP}{100}$

$= \frac{20\times450}{100}$

$=90$

SP $=$ CP $+$ Profit

SP $= 450 + 90$

SP $=Rs.\ 540$

Discount $ \% = 10 \%$

Therefore,

Marked price $= \frac{100 \times SP}{100-Discount \%}$

$=\frac{100\times540}{100-10}$

$= 100\times6$

$=Rs.\ 600$

The marked price of the article is Rs. 600.