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

$\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt\;and\;Gloves - Cost\;Price\;of\;Skirt\;and\;Gloves }{Cost\;Price\;of\;Skirt\;and\;Gloves}) \times 100 = 20}$

$\mathsf{\implies (\frac{48 - 4 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 100 = 20}$

$\mathsf{\implies (\frac{44 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 5 = 1}$

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

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

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

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

Profit Percentage on the Cost of the Skirt :

$\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt - Cost\;Price\;of\;Skirt}{Cost\;Price\;of\;Skirt}) \times 100}$

$\mathsf{\implies (\frac{40 - 36}{36}) \times 100}$

$\mathsf{\implies (\frac{4}{36}) \times 100}$

$\mathsf{\implies (\frac{1}{9}) \times 100}$

$\mathsf{\implies 11.11\%}$