The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is ₹ 2,400, find:

(i) its marked price

(ii) its selling price

(iii) the profit percent.

(i) Given:

C.P. = 25% below the M.P.

C.P. = ₹ 2,400

Let the M.P. be ₹ $x$.

$x - \dfrac{25}{100} \times x = 2,400\\[1em] \Rightarrow x - \dfrac{1}{4} \times x = 2,400\\[1em] \Rightarrow \dfrac{4x}{4} - \dfrac{x}{4} = 2,400\\[1em] \Rightarrow \dfrac{(4x - x)}{4} = 2,400\\[1em] \Rightarrow \dfrac{3x}{4} = 2,400\\[1em] \Rightarrow x = \dfrac{2,400 \times 4}{3}\\[1em] \Rightarrow x = \dfrac{9,600}{3}\\[1em] \Rightarrow x = ₹ 3,200$

Hence, the marked price = ₹ 3,200.

(ii) M.P. of the article = ₹ 3,200

Discount = 15% of M.P.

$\Rightarrow \dfrac{15}{100} \times ₹ 3,200\\[1em] \Rightarrow \dfrac{3}{20} \times ₹ 3,200\\[1em] \Rightarrow₹ \dfrac{9,600}{20}\\[1em] \Rightarrow₹ 480$

S.P. of the article = M.P. - Discount

= ₹ 3,200 - ₹480

= ₹ 2,720

Hence, the selling price = ₹ 2,720.

(iii) C.P. = ₹ 2,400

S.P. = ₹ 2,720

Profit = S.P. - C.P.

= $₹ 2,720 - ₹ 2,400$

= $₹ 320$

And,

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\\[1em] = \dfrac{320}{2400} \times 100\%\\[1em] = \dfrac{32000}{2400}\%\\[1em] = \dfrac{40}{3}\%\\[1em] = 13\dfrac{1}{3}\%$

Hence, the profit percent = $13\dfrac{1}{3}\%$.