A readymade garment shop in Delhi allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shopkeeper for Rs.400
(a) Rs. 600
(b) Rs. 650
(c) Rs. 700
(d) Rs. 750

Hint: Let the marked price of the product be Rs. x and the selling price be Rs. y. The first equation we get is by using the fact that the selling price is equal to cost price added with profit. The other equation we get is using the point that selling price is equal to list price minus the discount given. Equate the two to get the value of x.

Complete step by step solution:
Let us start the solution to the above question by letting the marked price of the product be Rs. x and the selling price be Rs. y.
Now, we know that the seller made a profit of 20% when he sold the product for Rs. y. For finding the profit we will subtract the net cost price by net selling price and divide the result by cost price and multiply the result by 100 to get it converted to percent. Also, it is given that the cost price is Rs. 400.
$profit=\dfrac{y-400}{400}\times 100$
$\Rightarrow 20=\dfrac{y-400}{400}\times 100$
$\Rightarrow 80=y-400$
$\Rightarrow y=Rs.\text{ }480..........(i)$
Also, we know that if we subtract the discount from the marked price, we get the selling price. So, if we represent this mathematically, we get
$x-\dfrac{20}{100}x=y$
Now we will substitute the value of y from equation (i). On doing so, we get
$\dfrac{80}{100}x=480$
$\Rightarrow x=Rs.\text{ 600}$
Hence, the answer to the above question is option (a).

Note: Don’t get confused and calculate the profit with respect to SP or discount with respect to CP. Always remember that the profit and loss are calculated with respect to cost price and discount is calculated with respect to selling price.