A trader bought some goods whose market price was £100,000 at a discount of 2.5%. After selling the goods the trader is required to pay tax at a rate of 20% on the profit she makes in excess of £10,000.How much should she sell the goods so that after tax she would make a profit of £20,000
MP = market price
SP = selling price
Tr = tax rate
MP = 100,ooo
SP = ?
Tr = 20 %
Discount = 2.5% = 2.5%*100,000 = 2,500
Buying price = BP = 100,000 – 2,500 = 97,500
Profit = Selling Price – Buying Price
P = SP – BP
Tax = Tax rate * profit greater than 10,000
Tx = 20%*(P – 10,000)
Net Profit = P – Tx = 20,000 (required net profit)
P - 20%(P – 10,000) = 20,000
P – 0.2P + 2,000 = 20,000
0.8P = 18,000
P = 22,500
But P = SP – BP
22,500 = SP – 97,500
SP = 120,000