By selling an article for ₹ 24, a man gains as much percent as its cost price. Find the cost price of the article.

Let cost price be ₹ x.

Profit = ₹ (24 - x)

According to question,

Profit percent = x%.

By formula,

$\Rightarrow \text{Profit \%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100 \\[1em] \Rightarrow x = \dfrac{24 - x}{x} \times 100 \\[1em] \Rightarrow x^2 = 100(24 - x) \\[1em] \Rightarrow x^2 = 2400 - 100x \\[1em] \Rightarrow x^2 + 100x - 2400 = 0 \\[1em] \Rightarrow x^2 + 120x - 20x - 2400 = 0 \\[1em] \Rightarrow x(x + 120) - 20(x + 120) = 0 \\[1em] \Rightarrow (x - 20)(x + 120) = 0 \\[1em] \Rightarrow x - 20 = 0 \text{ or } x + 120 = 0 \\[1em] \Rightarrow x = 20 \text{ or } x = -120.$

Since, C.P. cannot be negative.

∴ x = ₹ 20.

Hence, cost price = ₹ 20.