By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is ₹ 1,440, find :

(i) the marked price of the article.

(ii) the cost price of the article.

(i) Given:

Discount on the article = 20%

S.P. of the article = ₹ 1,440

Let the M.P. of the article be ₹$x$.

As we know,

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 20 = \dfrac{\text{Discount}}{x} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{20 \times x}{100}\\[1em] \Rightarrow \text{Discount} = \dfrac{20x}{100}\\[1em] \Rightarrow \text{Discount} = \dfrac{x}{5}\\[1em]$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{5} = x - 1440\\[1em] \Rightarrow 1440 = x - \dfrac{x}{5}\\[1em] \Rightarrow 1440 = \dfrac{5x}{5} - \dfrac{x}{5}\\[1em] \Rightarrow 1440 = \dfrac{(5x - x)}{5} \\[1em] \Rightarrow 1440 = \dfrac{4x}{5} \\[1em] \Rightarrow x = \dfrac{5 \times 1,440}{4} \\[1em] \Rightarrow x = \dfrac{7,200}{4} \\[1em] \Rightarrow x = 1,800$

Hence, M.P. of the article = ₹ 1,800

(ii) S.P. of the article = ₹ 1,440

Gain% of the article = 25%

Let the C.P. be ₹ $y$.

$\text{Gain \%} = \dfrac{\text{Gain}}{\text{C.P.}}\times 100\\[1em] \Rightarrow 25 = \dfrac{\text{Gain}}{y}\times 100\\[1em] \Rightarrow \text{Gain} = \dfrac{25 \times y}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{25y}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{y}{4}$

And,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{y}{4} = 1,440 - y\\[1em] \Rightarrow \dfrac{y}{4} + y = 1,440 \\[1em] \Rightarrow \dfrac{y}{4} + \dfrac{4y}{4} = 1,440 \\[1em] \Rightarrow \dfrac{(y + 4y)}{4} = 1,440 \\[1em] \Rightarrow \dfrac{5y}{4} = 1,440 \\[1em] \Rightarrow y = \dfrac{1,440 \times 4}{5} \\[1em] \Rightarrow y = \dfrac{5,760}{5} \\[1em] \Rightarrow y = 1,152$

Hence, C.P. of the article = ₹ 1,152