By selling an article for ₹ 704, a person loses 12%. Find his cost price and the loss.

Given:

S.P. = ₹ 704

Loss % = 12%

Let C.P. = $₹x$.

$\text{Loss \%} = \dfrac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$\Rightarrow 12 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{12 \times x}{100}\\[1em] = \dfrac{3x}{25}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{3x}{25} = x - 704\\[1em] \Rightarrow 704 = x - \dfrac{3x}{25}\\[1em] \Rightarrow 704 = \dfrac{25x}{25} - \dfrac{3x}{25}\\[1em] \Rightarrow 704 = \dfrac{(25x - 3x)}{25} \\[1em] \Rightarrow 704 = \dfrac{22x}{25}\\[1em] \Rightarrow x = \dfrac{25 \times 704}{22}\\[1em] \Rightarrow x = \dfrac{17,600}{22}\\[1em] \Rightarrow x = ₹ 800$

Loss = $\dfrac{3x}{25}$

Gain = $\dfrac{3 \times 800}{25}$

Gain = $\dfrac{2400}{25}$ = $96$

Hence, C.P. = ₹ 800 and loss = ₹ 96.