By selling an article for ₹ 1,200, Rohit loses one-fifth of its cost price. For how much should he sell it in order to gain 30% ?

Given:

S.P. of an article = ₹ 1,200

Loss = one-fifth of C.P.

Let C.P. of the article = ₹ $x$.

Loss = $\dfrac{1}{5} \times x$

= $\dfrac{x}{5}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{5} = x - 1,200\\[1em] \Rightarrow 1,200 = x - \dfrac{x}{5}\\[1em] \Rightarrow 1,200 = \dfrac{5x}{5} - \dfrac{x}{5}\\[1em] \Rightarrow 1,200 = \dfrac{(5x - x)}{5} \\[1em] \Rightarrow 1,200 = \dfrac{4x}{5}\\[1em] \Rightarrow x = \dfrac{1,200 \times 5}{4}\\[1em] \Rightarrow x = \dfrac{6,000}{4}\\[1em] \Rightarrow x = 1,500$

Hence, C.P. of the article = ₹ 1,500

Gain % = 30%

$\text{Gain \%} = \dfrac{\text{Gain}}{\text{C.P.}} \times \text{100}\\[1em] \Rightarrow 30 = \dfrac{\text{Gain}}{1,500} \times 100\\[1em] \Rightarrow \text{Gain} = \dfrac{30 \times 1,500}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{45,000}{100}\\[1em] \Rightarrow \text{Gain} = 450$

And,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 450 = \text{S.P.} - 1,500\\[1em] \Rightarrow \text{S.P.} = 450 + 1,500\\[1em] \Rightarrow \text{S.P.} = 1,950$

Hence, New S.P. of the article = ₹ 1,950.