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Mathematics

The marked price of a toy is same as the percentage of GST that is charged. The price of the toy is ₹ 24 including GST. Taking the marked price as x, form an equation and solve it to find x.

Quadratic Equations

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Answer

Given,

M.P. of toy = ₹ x

G.S.T. charged = x%

Price including G.S.T. = ₹ 24

∴24=x+x100×x⇒24=x+x2100⇒24=100x+x2100⇒2400=x2+100x⇒x2+100x−2400=0⇒x2+120x−20x−2400=0⇒x(x+120)−20(x+120)=0⇒(x−20)(x+120)=0⇒x−20=0 or x+120=0⇒x=20 or x=−120\therefore 24 = x + \dfrac{x}{100} \times x \\[1em] \Rightarrow 24 = x + \dfrac{x^2}{100} \\[1em] \Rightarrow 24 = \dfrac{100x + x^2}{100} \\[1em] \Rightarrow 2400 = x^2 + 100x \\[1em] \Rightarrow x^2 + 100x - 2400 = 0 \\[1em] \Rightarrow x^2 + 120x - 20x - 2400 = 0 \\[1em] \Rightarrow x(x + 120) - 20(x + 120) = 0 \\[1em] \Rightarrow (x - 20)(x + 120) = 0 \\[1em] \Rightarrow x - 20 = 0 \text{ or } x + 120 = 0 \\[1em] \Rightarrow x = 20 \text{ or } x = -120

Since, M.P. cannot be negative.

∴ M.P. = ₹ 20 and G.S.T. = 20%.

Hence, the marked price of toy = ₹ 20 and G.S.T. = 20%.

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