A shopkeeper sold an item at 10% loss after giving a discount equal to half the marked price. Then the cost price is ?

Let the cost price = Rs. 100
Selling price = Rs. 90
Marked price = 90 × 2 = Rs. 180
(∴ Selling price will be half of the Marked price as the discount is also equal to half the Marked price)
$$ \Rightarrow \frac{{{\text{Cost price }}}}{{{\text{Marked price}}}}$$   $$ = \frac{{100}}{{180}}$$   $$ = \frac{5}{9}$$
$$ \Rightarrow {\text{Cost price = }}$$   $$\frac{5}{9}{\text{ of Marked price}}$$