By selling an article for ₹ 900, a man gains 20%. Find his cost price and the gain.

Given:

S.P. = ₹ 900

Gain % = 20%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 20 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{20 \times x}{100}\\[1em] = \dfrac{x}{5}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{5} = 900 - x\\[1em] \Rightarrow 900 = \dfrac{x}{5} + x\\[1em] \Rightarrow 900 = \dfrac{x}{5} + \dfrac{5x}{5}\\[1em] \Rightarrow 900 = \dfrac{(x + 5x)}{5} \\[1em] \Rightarrow 900 = \dfrac{6x}{5}\\[1em] \Rightarrow x = \dfrac{5 \times 900}{6}\\[1em] \Rightarrow x = \dfrac{4500}{6}\\[1em] \Rightarrow x = 750$

Gain = $\dfrac{x}{5}$

Gain = $\dfrac{750}{5}$ = 150

Hence, C.P. = ₹ 750 and gain = ₹ 150.