Question

Molly bought a pair of gloves and a skirt. The gloves cost £4. She sold teh gloves and the skirt for a total of £48. She made 100% profit on the cost of the gloves. 20% profit on the total cost. Work out the percentage profit on the cost of the skirt

Answer 1

Given : Molly bought a pair of Gloves which cost £4

Given : Molly sold the Gloves and Skirt for a Total of £48

Given : Molly made 100% Profit on the Cost of the Gloves

⇒ Molly sold the Gloves at a Cost of £8

Selling Price of Gloves + Selling Price of Skirt = £48

⇒ £8 + Selling Price of Skirt = £48

⇒ Selling Price of Skirt = £40

Given : Molly made 20% Profit on the Total Cost

`\mathsf{\implies ((Selling\;Price\;of\;Skirt\;and\;Gloves - Cost\;Price\;of\;Skirt\;and\;Gloves )/(Cost\;Price\;of\;Skirt\;and\;Gloves)) * 100 = 20}`

`\mathsf{\implies ((48 - 4 - Cost\;Price\;of\;Skirt)/(4 + Cost\;Price\;of\;Skirt)) * 100 = 20}`

`\mathsf{\implies ((44 - Cost\;Price\;of\;Skirt)/(4 + Cost\;Price\;of\;Skirt)) * 5 = 1}`

`\mathsf{\implies 5(44 - Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}`

`\mathsf{\implies 220 - 5(Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}`

`\mathsf{\implies 6(Cost\;Price\;of\;Skirt) = 216}`

`\mathsf{\implies (Cost\;Price\;of\;Skirt) = 36}`

Profit Percentage on the Cost of the Skirt :

`\mathsf{\implies ((Selling\;Price\;of\;Skirt - Cost\;Price\;of\;Skirt)/(Cost\;Price\;of\;Skirt)) * 100}`

`\mathsf{\implies ((40 - 36)/(36)) * 100}`

`\mathsf{\implies ((4)/(36)) * 100}`

`\mathsf{\implies ((1)/(9)) * 100}`

`\mathsf{\implies 11.11\%}`