A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of 5% to a buyer. If the buyer pays Rs. 451.44 for the article inclusive of GST at 18%, find :
(i) the printed price of the article.
(ii) the profit percentage of retailer.

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Solution

Step 1: Given information:
Discount on retailer purchase $= 15 %$
The mark-up by retailer $= 10 %$
Cost price of buyer inclusive GST $= Rs . 451.44$
Step 2: Calculate printed price of the article:
Let print price of article be $Rs . x$
The retailer cost price is computed as;
$C . P = x - (15 % of x) C . P = x - \frac{15}{100} x C . P = \frac{85}{100} x$
Since, retailer mark-up the price by 10%.
Therefore, marked price for retailer;
$Marked price = x + \frac{10}{100} x Marked price = \frac{11}{10} x$
The retailer allows a discount of 5% to a buyer.
$Sale price = \frac{11}{10} x \times \frac{(100 - 5)}{100} Sale price = \frac{209}{200} x$
Sale price inclusive GST;
$S . P = \frac{209}{200} x + (\frac{18}{100} \times \frac{209}{200} x) S . P = \frac{209}{200} x \times \frac{118}{100}$
It is given that, the buyer pays Rs. 451.44 for the article inclusive of GST.
Therefore,
$\frac{209}{200} x \times \frac{118}{100} = 451.44 \Rightarrow x = \frac{451.44 \times 100 \times 200}{209 \times 118} \Rightarrow x = Rs . 366.1$
The printed price of the article is Rs. 366.1
Step 3: Calculate retailer profit percentage:
$C . P = \frac{85}{100} x = \frac{85}{100} \times 366.1 = Rs . 311.18 S . P = \frac{209}{200} x = \frac{209}{200} \times 366.1 = Rs . 382.57 Profit % = \frac{S . P - C . P}{C . P} \times 100 Profit % = \frac{382.57 - 311.18}{311.18} \times 100 Profit % = \frac{71.39}{311.18} \times 100 Profit % = 22.94 %$
Final Answer:
(i) The printed price of article is $Rs . 366.1$
(ii) The profit percent of retailer is $22.94 %$

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