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