A shopkeeper allows 23% commision on his advertised price and still makes a profit of 10%.

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 .