Question

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.

Answer 1

Given,

C.P. = ₹ x

S.P. = ₹ 27

Loss = (x − 5) %

Loss = C.P. − S.P.

= ₹ (x − 27)

As we know that Loss % = `"Loss"/"C.P." × 100`

Substituting the values, we get

⇒ `(x - 5) = ((x - 27))/x xx 100`

⇒ x(x − 5) = (x − 27) × 100

⇒ x² − 5x = 100x − 2700 

⇒ x² − 5x − 100x + 2700 = 0 

⇒ x² − 105x + 2700 = 0 

⇒ x² − 45x − 60x + 2700 = 0

⇒ x(x − 45) − 60(x − 45) = 0

⇒ (x − 45)(x − 60) = 0

⇒ (x − 45) = 0 or (x − 60) = 0

⇒ x = 45 or x = 60

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