Question

Jai bought a helmet and a pair of skates.

The helmet cost £45.
He sold both items for £224.
Jai made a 120% profit on the cost of the helmet and a 40% profit on the total cost.
What was the percentage profit on the skates?
Give your answer to 1 decimal place.

Answer 1

Profit % on skates = 8.7 %

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%

`Profit \% = (Selling \ price - cost \ price )/(Cost \ price) * 100`

`(40)/(100) = (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 = (22400)/(140)\\\\x = 160 - 45 = \£ \ 115`

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 %

`Profit \% = (selling \ price - cost \ price)/(cost \ price)`

`(120)/(100) = (y -45)/(45)\\\\(120 * 45)/(100) = y -45\\\\54 = y - 45\\\\99 = y`

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

`Profit \% \ on \ skates = (selling\ price- cost \ price )/(cost \ price) * 100`

`= (125-115)/(115) * 100\\\\=(10)/(115) * 100\\\\= 8.7 \%`