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Mathematics

John purchased a movie camera for ₹25488, which includes 10% rebate on the list price and 18% tax (under GST) on the remaining price. Find the marked price of the camera.

GST

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Answer

Given:

Rate of GST = 18%

Rebate (or discount) = 10% on Marked Price

Let the marked price be be P

Cost price of the article = Marked Price - Discount

=P−10% of P=P−(10100)×P=100P−10P100=90P100=0.9P= \text{P} - 10\% \text{ of P} \\[1em] = \text{P} - \Big(\dfrac{10}{100}\Big) \times \text{P} \\[1em] = \dfrac{100\text{P} - 10\text{P}}{100} \\[1em] = \dfrac{90\text{P}}{100} \\[1em] = 0.9\text{P}

Amount of GST on cost price of article = 18% of 0.9P

Amount paid by John = Cost Price + GST = 25488

⇒0.9P+(18100×0.9P)=25488⇒0.9P+0.162P=25488⇒1.062P=25488⇒P=254881.062=₹24000\Rightarrow 0.9\text{P}+ \Big(\dfrac{18}{100}\times0.9\text{P}\Big) = 25488 \\[1em] \Rightarrow 0.9\text{P}+ 0.162\text{P} = 25488 \\[1em] \Rightarrow 1.062\text{P} = 25488 \\[1em] \Rightarrow \text{P} = \dfrac{25488}{1.062} = \bold{₹24000}

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