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

Answer: Option C

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)
$$\Rightarrow \frac{\text{Cost price }}{\text{Marked price}}$$   $$=\frac{100}{180}$$   $$=\frac{5}{9}$$
$$\Rightarrow \text{Cost price = }$$   $$\frac{5}{9}\text{ of Marked price}$$