Question

A merchant purchased a line of handbags for 30$ each. She wanted to offer a 10% discount off the listed selling price and still make a 20% profit. What price should she mark on the label?

Answer 1

The merchant spent 30$ to buy the bag. 20% of this price is

$\dfrac{20}{100}\cdot 30=6$

So, he has to sell the bag at 36$.

This is not the selling price, but its 90%, because of the 10% discount.

So, the label price is such that

$\dfrac{90}{100}x=36 \iff x=\dfrac{3600}{90}=40$

So, the merchant will declare a price of $40.

After the 10% discount, the price will drop to $36.

If she sells the bag for $36, her profit will be $36 - $30 = $6, which is 20% of 30 as required.