Question

Molly bought a pair of gloves and a skirt. The gloves cost £4. She sold the gloves and the skirt for a total of £48. She made1100% profit on the cost of the gloves and 20% profit on the total cost. Work out her percentage profit on the cost of the skirt. Give your answer to one decimal place

Answer 1

Answer:

11.1%

Step-by-step explanation:

Given:

Molly bought a pair of gloves and a skirt.

The gloves cost £4.

She sold the gloves and the skirt for a total of £48.

She made 100% profit on the cost of the gloves and 20% profit on the total cost.

Question asked:

Percentage profit on the cost of the skirt = ?

Solution:

Cost price of gloves = £4

Profit % = 100

Profit amount = $100\%\ of 4=4$

Sell price of gloves = Cost price + Profit amount

                                =  £4 + £4 = £8

Sell price of both gloves and skirt = £48

Sell price of skirt = £48 -  £8 =  £40

As given, she makes 20% profit on the total cost.

Let cost price of skirt = $x$

Cost price of  both gloves and skirt = $4+x$

Total Profit = $20\%\ of\ (4+x)=\frac{20}{100} \times(4+x)=\frac{1}{5} \times(4+x)=\frac{4}{5} +\frac{x}{5}$

Sell price of both gloves and skirt =  Cost price of both gloves and skirt + Total profit

$48=(4+x)+(\frac{4}{5} +\frac{x}{5} )$

$48=4+\frac{4}{5} +x+\frac{x}{5} \\\\ 48=\frac{24}{5} +\frac{6x}{5} \\\\ 48=\frac{24+6x}{5}$

By cross multiplication:

By subtracting both sides by 24

$216=6x$

By dividing both sides by 6

$x=36$

Cost price of skirt = $x$ = £36

Profit = Sell price of skirt - Cost price of skirt

         = £40 - £36 = £4

Profit% = $\frac{Profit}{Cost\ price} \times100$

            = $\frac{4}{36} \times100=\frac{400}{36} =11.111\%=11.1\%$

Therefore,  percentage profit on the cost of the skirt is 11.1%