Profit and Loss : Arithmetic

Question

Profit on selling 10 Apples equals selling price of 3 Bananas. While loss on selling 10 Bananas equals selling price of 4 Apples. Also profit percent-age equals to the loss percentage and cost of an Apple is half of the cost of a Banana. What is the ratio of selling price of Apple to the selling price of a Banana?

Cost price of apple=a

Cost price of banana=2a

Selling Price of apple=A

Selling Price of banana=B

$$10(A-a)=3B$$

$$10(2a-B)=4A \tag 2$$

$$\frac{A-a}{a}=\frac{2a-B}{2a}$$

$=>2A+B=4a \tag 4$

If I place 4 in 2, I get

$$10(A-\frac{2A+B}{4})=3B$$

Solving the above equation , I get

A:B=11:10

In which step am I wrong?

Answer 1

From 1st and 2nd we have :

$\dfrac A B = \dfrac 3 4 \dfrac {2a−B}{A−a}$.

From 3rd we have :

$\dfrac {2a−B}{A−a} = 2$.

Substituting we get :

$\dfrac A B = \dfrac 3 4 \times 2 = \dfrac 3 2$.