A trader bought an article for ₹ x and sold it for ₹ 52, thereby making a profit of (x - 10) percent on his outlay. Calculate the cost price.

C.P. = ₹ x

S.P. = ₹ 52

Profit = S.P. - C.P. = ₹(52 - x)

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

Substituting value in above equation we get,

$\Rightarrow x - 10 = \dfrac{52 - x}{x} \times 100 \\[1em] \Rightarrow x(x - 10) = 100(52 - x) \\[1em] \Rightarrow x^2 - 10x = 5200 - 100x \\[1em] \Rightarrow x^2 - 10x + 100x - 5200 = 0 \\[1em] \Rightarrow x^2 + 90x - 5200 = 0 \\[1em] \Rightarrow x^2 + 130x - 40x - 5200 = 0 \\[1em] \Rightarrow x(x + 130) - 40(x + 130) = 0 \\[1em] \Rightarrow (x - 40)(x + 130) = 0 \\[1em] \Rightarrow (x - 40) = 0 \text{ or } (x + 130) = 0 \\[1em] \Rightarrow x = 40 \text{ or } x = -130.$

Since, cost cannot be negative

∴ x ≠ -130.

Hence, C.P. = ₹ 40