The C.P. of an article is ₹ x which is sold for ₹ 27 at a loss of (x - 5) percent; find the value of x.

Given,

C.P. = ₹ x

S.P. = ₹ 27

Loss = (x - 5) %

Loss = C.P. - S.P.

= ₹ (x - 27)

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

Substituting the values, we get

$\Rightarrow (x - 5) = \dfrac{(x - 27)}{x} \times 100 \\[1em] \Rightarrow x(x - 5) = (x - 27) \times 100 \\[1em] \Rightarrow x^2 - 5x = 100x - 2700 \\[1em] \Rightarrow x^2 - 5x - 100x + 2700 = 0\\[1em] \Rightarrow x^2 - 105x + 2700 = 0\\[1em] \Rightarrow x^2 - 45x - 60x + 2700 = 0\\[1em] \Rightarrow x(x - 45) - 60(x - 45) = 0\\[1em] \Rightarrow (x - 45)(x - 60) = 0\\[1em] \Rightarrow (x - 45) = 0 \text{ or } (x - 60) = 0\\[1em] \Rightarrow x = 45 \text{ or } x = 60\\[1em]$

Hence, the value of C.P. = ₹ 45 or ₹ 60.