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 sales tax (under VAT) at 8%. find the printed price of the article.
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%