Question

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

Answer 1

Given,

C.P. = ₹ x

S.P. = ₹ 152

Profit = (x + 10) %

Profit = S.P. − C.P.

= ₹ (152 − x)

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

Substituting the values, we get

⇒ `(x + 10) = ((152 - x))/x xx 100`

⇒ x(x + 10) = (152 − x) × 100

⇒ x² + 10x = 15200 − 100x

⇒ x² + 10x − 15200 + 100x = 0

⇒ x² + 110x − 15200 = 0

⇒ x² + 190x − 80x − 15200 = 0

⇒ x(x + 190) − 80(x + 190) = 0

⇒ (x + 190)(x − 80) = 0

⇒ (x + 190) = 0 or (x − 80) = 0

⇒ x = −190 or x = 80

The cost price of the article cannot be negative.

Hence, the value of C.P. = ₹ 80.