Question

19. If the cost price of 18 apples is the same as selling price of 16 apples, what is the profit in $ as well as percentage gain?

Answer 1

Percent Gain = 12.5%

Step-by-step explanation

We are told that the

cost price of 18 apples = selling price of 16 apples

Let the cost price of an apple be x dollars

Let the selling price of an apple be y dollars

Buying 18 apples will cost 18 × x = (18x) dollars

Selling 16 apples will bring in 16 × y = (16y) dollars

Recall,

cost price of 18 apples = selling price of 16 apples

18x = 16y

We can rewrite as

16y = 18x

Divide both sides by 16

(16y/16) = (18x/16)

y = 1.125x

Percent gain is calculated as

`\text{Percent Gain = }\frac{(\text{Selling price)-(Cost price)}}{Cost\text{ price}}*100\text{ percent}`

Selling price = y

Cost price = x

But recall that

y = 1.125x

`\begin{gathered} \text{Percent Gain = }(y-x)/(x)*100\text{ percent} \\ =(1.125x-x)/(x)*100\text{ percent} \\ =(0.125x)/(x)*100\text{ percent} \\ =0.125*100\text{ percent} \\ =12.5\text{ percent} \end{gathered}`

Hope this Helps!!!