Retailer buys an article at a discount of 15% on the printed price from a wholesaler he marks of the price by 10% on the printed price but due to the 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 rupees for the article inclusive of tax under gst find the printed price of the article andfor the article inclusive of tax under gst find the printed price of the article and the profit percent of the retailer
Answers
(i) The printed price of the article is ₹ x
The seller notes the price by 10% on the printed price
Therefore, the price marked by the seller = ₹ x + 10% of x
= ₹ x + ₹ 0.1x
= ₹ 1.1x
Due to competition the seller allows a 5% discount on the marked price, then
Sale price of article = ₹ 1.1x - discount
Discount = 5% of x 1.1x
= ₹ (5/100) x 1.1x
= ₹ 0.055x
GST rate = 12%
Purchase (under GST) for purchase = 12% of the sale price set by the seller
= 12% by ₹ (1.1x - 0.055x)
= ₹ (12/100) x (1.045x)
Therefore, the price of the article includes GST = ₹ 1.045x + ₹ (12/100) x (1.045x)
Given, the buyer pays ₹ 468.16 for a taxable article (under GST)
Therefore,
1.045x + (12/100) x (1.045x) = 468.16
1.045x + 0.1254x = 468.16
1.1704x = 468.16
x = 468.16 / 1.1704
x = ₹ 400
Therefore, the printed price of the article is ₹ 400
(ii) The seller buys at a discount of 15% of the printed price and sells for 5% of the discounted price of 10% at the printed price
Therefore,
Purchased at 400 - 15% of ₹ 400 = ₹ 400 - ₹ 60 = ₹ 340
Sold to = (₹ 400 + 10% of ₹ 400) - 5% of (₹ 400 + 10% of ₹ 400)
= ₹ (400 + 40) - [(5/100) x ₹ 400 + 40)]
= ₹ 440 - ₹ (0.05 x 440)
= ₹ 440 - ₹ 22
= ₹ 418
Therefore, profit = Sale price - price = ₹ 418 - ₹ 340 = ₹ 78
Therefore, profit percentage = (78/340) x 100 = 22.94%