By selling an article for ₹ 96, a man gains as much percent as its cost price. Find the cost price of the article.

Let cost price be ₹ x.

S.P. = ₹ 96

Profit = S.P. - C.P. = ₹ (96 - x)

Given,

Man gains as much percent as its cost price.

Profit percent = x %.

Substituting values we get :

$\Rightarrow \dfrac{\text{Profit}}{\text{C.P.}} \times 100 = x \\[1em] \Rightarrow \dfrac{96 - x}{x} \times 100 = x \\[1em] \Rightarrow 100(96 - x) = x^2 \\[1em] \Rightarrow x^2 = 9600 - 100x \\[1em] \Rightarrow x^2 + 100x - 9600 = 0 \\[1em] \Rightarrow x^2 + 160x - 60x - 9600 = 0 \\[1em] \Rightarrow x(x + 160) - 60(x + 160) = 0 \\[1em] \Rightarrow (x - 60)(x + 160) = 0 \\[1em] \Rightarrow x - 60 = 0 \text{ or } x + 160 = 0 \\[1em] \Rightarrow x = 60 \text{ or } x = -160.$

Since, cost price cannot be negative.

∴ x = 60.

Hence, C.P. = ₹ 60.