Step-by-step explanation:
Cost of hat = £10
Michael made 200% profit on the hat.
[tex]\texttt{Selling price of hat = }10+\frac{200}{100}\times 10=30[/tex]
He sold both items for a total of £90.
Selling price of coat = 90 - 30 = £60
He made 80% profit on the total cost. Let C be the cost for coat and hat.
That is
[tex]C+\frac{80}{100}\times C=90\\\\1.8C=90\\\\C=50[/tex]
Cost for coat = 50 - 10 = £40
[tex]\texttt{Percentage profit on the cost of the coat = }\frac{60-40}{40}\times 100\\\\\texttt{Percentage profit on the cost of the coat = }50\%[/tex]
Percentage profit on the cost of the coat is 50 %
