A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10% on the printed price but due to competition in the market, he allows a discount of 5% on the marked price to a buyer. If the rate of GST is 12% and the buyer pays ₹468.16 for the article inclusive of tax (under GST), find

(i) the printed price of the article.

(ii) the profit percentage of the retailer.

Given:

Rate of GST = 12%

Discount for retailer = 15% on Printed Price

Let the printed price be be P

Cost price of the article for retailer = Printed Price - Discount

$= \text{P} - 15\% \text{ of P } \\[1em] = \text{P} - \Big(\dfrac{15}{100}\Big) \times \text{P} \\[1em] = \dfrac{100\text{P} - 15\text{P}}{100} \\[1em] = \dfrac{85\text{P}}{100} \\[1em] = 0.85\text{P} \\[1em]$

Amount of GST on cost price of article paid by retailer (or collected by the wholesaler)

$= 12\% \text{ of } 0.85 \text{P} \\[1em] = \dfrac{12}{100}\times{0.85\text{P}} \\[1em] = 0.102\text{P}$

Since the retailer marks the price at 10% premium on printed price = Marked Price = Printed Price + Premium

$= \text{P} + 10\% \text{ of P} \\[1em] = \text{P} + \Big(\dfrac{10}{100} \times P\Big) \\[1em] = \dfrac{\text{100P} + \text{10P}}{100} \\[1em] = \dfrac{110\text{P}}{100} \\[1em] = 1.1\text{P}$

Discount given by retailer on marked price to the buyer = 5%

$= 5\% \text{ of Marked Price} \\[1em] = 5\% \text{ of } 1.1\text{P} \\[1em] = \dfrac{5}{100}\times{1.1\text{P}} \\[1em] = \dfrac{5.5\text{P}}{100} \\[1em] = 0.055\text{P}$

Cost Price of the article for the buyer = Marked Price- Discount

$= 1.1\text{P} - 0.055\text{P} \\[1em] = 1.045\text{P}$

Amount of GST on cost price of article paid by buyer (or collected by the retailer)

$= 12\% \text{ of } 1.045\text{P} \\[1em] = \dfrac{12}{100}\times{1.045\text{P}} \\[1em] = 0.1254\text{P}$

(i) The printed price of the article.

Amount paid by buyer for the article = Cost Price + GST = 468.16

$\Rightarrow 1.045\text{P} + 0.1254\text{P} = 468.16 \\[1em] \Rightarrow 1.1704\text{P} = 468.16 \\[1em] \Rightarrow \text{P} = \dfrac{468.16}{1.1704} = \bold{₹400}$

(ii) The profit percentage of the retailer.

Cost Price of the article for the buyer = 1.045P = 1.045 x 400 = ₹418

Cost Price of the article for the retailer = 0.85P = 0.85 x 400 = ₹340

Profit of the retailer = Selling Price of the article for the retailer (or cost price of buyer) - Cost price of the article for the retailer
= 418 - 340 = ₹78

Profit % of the retailer $= \dfrac{\text{Profit}}{\text{Cost}}\times{100} \\[1em] = \dfrac{78}{340}\times{100} \\[1em] = \dfrac{390}{17} \\[1em] = \bold{22\dfrac{16}{17}}\%$