The C.P. of an article is ₹ x which is sold for ₹ 152 at a profit of (x + 10)%. Find the value of x.

Given,

C.P. = ₹ x

S.P. = ₹ 152

Profit = (x + 10) %

Profit = S.P. - C.P.

= ₹ (152 - x)

As we know that Profit % = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$

Substituting the values, we get

$\Rightarrow (x + 10) = \dfrac{(152 - x)}{x} \times 100 \\[1em] \Rightarrow x(x + 10) = (152 - x) \times 100 \\[1em] \Rightarrow x^2 + 10x = 15200 - 100x \\[1em] \Rightarrow x^2 + 10x - 15200 + 100x = 0\\[1em] \Rightarrow x^2 + 110x - 15200 = 0\\[1em] \Rightarrow x^2 + 190x - 80x - 15200 = 0\\[1em] \Rightarrow x(x + 190) - 80(x + 190) = 0\\[1em] \Rightarrow (x + 190)(x - 80) = 0\\[1em] \Rightarrow (x + 190) = 0 \text{ or } (x - 80) = 0\\[1em] \Rightarrow x = -190 \text{ or } x = 80\\[1em]$

The cost price of the article cannot be negative.

Hence, the value of C.P. = ₹ 80.