Problems on Quadratic Equations — Analytical & Application Based Questions

The Marked price of 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.

Answer

Given,

M.P. of toy = ₹ x

G.S.T. charged = x%

Price including G.S.T. = ₹ 24

∴ 24 = x + $\dfrac{x}{100}$ × x

⇒ 24 = x + $\dfrac{x^2}{100}$

⇒ 24 = $\dfrac{100x + x^2}{100}$

⇒ 2400 = 100x + x²

⇒ 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

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%.