The list price of an article is ₹ 800 and is available at a discount of 15 percent. Find :

(i) the selling price of the article;

(ii) the cost price of the article if a profit of $13\dfrac{1}{3}\%$ is made on selling it.

(i) Given:

M.P. of an article = ₹ 800

Discount of the article = 15%

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 15 = \dfrac{\text{Discount}}{800} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{15 \times 800}{100}\\[1em] = \dfrac{12000}{100}\\[1em] = 120$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 120 = 800 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 800 - 120\\[1em] \Rightarrow \text{S.P.} = 680$ Hence, S.P. of the article = ₹ 680.

(ii) S.P. of the article = ₹ 680

Profit = $13\dfrac{1}{3}\%$ = $\dfrac{40}{3}\%$

Let the C.P. be ₹ $x$.

As we know,

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \dfrac{40}{3} = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{40 \times x}{3 \times 100}\\[1em] = \dfrac{40x}{300}\\[1em] = \dfrac{2x}{15}\\[1em]$

And,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{2x}{15} = 680 - x\\[1em] \Rightarrow \dfrac{2x}{15} + x = 680\\[1em] \Rightarrow \dfrac{2x}{15} + \dfrac{15x}{15} = 680\\[1em] \Rightarrow \dfrac{(2x + 15x)}{15} = 680\\[1em] \Rightarrow \dfrac{17x}{15} = 680\\[1em] \Rightarrow x = \dfrac{680 \times 15}{17}\\[1em] \Rightarrow x = \dfrac{10,200}{17}\\[1em] \Rightarrow x = 600\\[1em]$

Hence, C.P. of the article = ₹ 600.