A ready-made garments 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 ₹ 400.

Given:

C.P. of a dress = ₹ 400

Profit of the dress = 20%

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\\[1em] \Rightarrow 20 = \dfrac{\text{Profit}}{400} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{20 \times 400}{100}\\[1em] = \dfrac{8000}{100}\\[1em] = 80\\[1em]$

And,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 80 = \text{S.P.} - 400\\[1em] \Rightarrow \text{S.P.} = 80 + 400\\[1em] = 480$

S.P. of the dress = ₹ 480

Discount on the dress = 20%

Let the M.P. of the dress = ₹ $x$.

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 480$

And,

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 20 = \dfrac{(x - 480)}{x} \times 100\\[1em] \Rightarrow 20 \times x = (x - 480) \times 100\\[1em] \Rightarrow 20x = 100x - 48000\\[1em] \Rightarrow 48000 = 100x - 20x \\[1em] \Rightarrow 48000 = 80x \\[1em] \Rightarrow x = \dfrac{48000}{80} \\[1em] \Rightarrow x = 600$

Hence, M.P. of the dress = ₹ 600.