By selling an article for ₹ 1,200; Rohit gains one-fifth of its cost price. What should be the selling price of the article when he sells it at 30% gain?

Given:

S.P. of an article = ₹ 1,200

Gain = one-fifth of C.P.

Let C.P. of the article = ₹ $x$.

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

= $\dfrac{x}{5}$

As we know:

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

Hence, C.P. of the article = ₹ 1,000

Gain % = 30%

$\text{Gain \%} = \dfrac{\text{Gain}}{\text{C.P.}} \times \text{100}\\[1em] \Rightarrow 30 = \dfrac{\text{Gain}}{1,000} \times 100\\[1em] \Rightarrow \text{Gain} = \dfrac{30 \times 1,000}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{30,000}{100}\\[1em] \Rightarrow \text{Gain} = ₹ 300$

And,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 300 = \text{S.P.} - 1,000\\[1em] \Rightarrow \text{S.P.} = 300 + 1,000\\[1em] \Rightarrow \text{S.P.} = ₹ 1,300$

Hence, S.P. of the article = ₹ 1,300.