Question

Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.

Answer 1

The cost price of saree = Rs. 60x

and selling price = Rs. (500 + 4x)

Loss = x%

Now, according to the condition

S.P. = C.P. × `(100 - "Loss"%)/(100)`

500 + 4x = `(60x(100 - x))/(100)`

⇒ 50000 + 400x = 6000x - 60x²

⇒ 60x² - 6000x + 400x + 50000 = 0

⇒ 60x² - 5600x + 50000 = 0

⇒ 3x² - 280x + 2500 = 0              ...(Dividing by 20)

⇒ 3x² - 30x - 250x + 2500 = 0

⇒ 3x(x - 10) - 250(x - 10) = 0

⇒ (x - 10)(3x - 250) = 0

Either x - 10 = 0,

then x = 10

or

3x - 250 = 0,

then 3x = 250

⇒ x = `(250)/(3)`

But it is not possible

∴ Loss = 10%

Cost price = 60x

= 60 × 10

= Rs. 600