Question:
A shopkeeper allows 23% commision on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find his advertised price.
Solution:
Let the CP of the item be Rs. $x$.
Profit $=10 \%$
$\mathrm{SP}=\mathrm{CP}\left(\frac{100+\text { Profit } \%}{100}\right)$
$\mathrm{SP}=x\left(\frac{110}{100}\right)$
$\mathrm{SP}=$ Rs. $1.1 x$
Again, Profit $=\mathrm{SP}-\mathrm{CP}$
Therefore, Profit $=$ Rs. $(1.1 x-x)$
$=$ Rs. $0.1 x$
We get,
$0.1 x=56$
$x=$ Rs. 560
Now, the advertise $d$ price $=\frac{1.1 x}{1-0.23}$
$=$ Rs. $\frac{560 \times 1.1}{0.77}$
$=$ Rs. 800
Therefore, the advertised price of the item is Rs. 800 .