Answer:
Profit % on skates = 8.7 %
Step-by-step explanation:
Step 1 : Find cost price of skates
Cost price of helmet = £45
Let cost price of skate be = x
Selling price = £224
Cost price = (x + 45)
Total profit % = 40%
[tex]Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100[/tex]
[tex]\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115[/tex]
Total cost price = 45 + 115 = £160
Step 2 : Selling price of Helmet
Cost price of Helmet = £45
Let selling price of helmet be = y
Profit % of helmet = 120 %
[tex]Profit \% = \frac{selling \ price - cost \ price}{cost \ price}[/tex]
[tex]\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y[/tex]
Step 3 : Selling price of skates
Total selling = selling price of helmet + selling price of skates
224 = 99 + selling price of skates
224 - 99 = selling price of skates
125 = selling price of skates
Step 4 : Profit percentage on skates
Cost price of skate = £ 115
Selling price of skate = £ 125
[tex]Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100[/tex]
[tex]= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%[/tex]
