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Mathematics

A man bought an article for ₹ x and sold it for ₹ 16. If his loss was x percent, find the cost price of the article.

Quadratic Equations

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Answer

C.P. = ₹ x

S.P. = ₹ 16

Loss = ₹(x - 16)

Loss % = LossC.P.×100\dfrac{\text{Loss}}{\text{C.P.}} \times 100

Substituting value in above equation we get,

⇒x=x−16x×100⇒x2=100(x−16)⇒x2=100x−1600⇒x2−100x+1600=0⇒x2−80x−20x+1600=0⇒x(x−80)−20(x−80)=0⇒(x−20)(x−80)=0⇒x−20=0 or x−80=0⇒x=20 or x=80.\Rightarrow x = \dfrac{x - 16}{x} \times 100 \\[1em] \Rightarrow x^2 = 100(x - 16) \\[1em] \Rightarrow x^2 = 100x - 1600 \\[1em] \Rightarrow x^2 - 100x + 1600 = 0 \\[1em] \Rightarrow x^2 - 80x - 20x + 1600 = 0 \\[1em] \Rightarrow x(x - 80) - 20(x - 80) = 0 \\[1em] \Rightarrow (x - 20)(x - 80) = 0 \\[1em] \Rightarrow x - 20 = 0 \text{ or } x - 80 = 0 \\[1em] \Rightarrow x = 20 \text{ or } x = 80.

Hence, C.P. = ₹ 20 or ₹ 80.

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