How much does the fruit concentrate cost in $1$ liter of fruit juice? In a factory, $1$ liter of fruit juice contains water cost, fruit concentrate cost and packing cost. 


*

*There's fruit concentrate $\%25$ of water in the fruit concentrate and water mixture. 

*Water cost equals $\%30$ of  fruit concentrate cost. 

*Packing cost is $0.32\$$
If you sell $1$ liter of fruit juice with the price of $2.4\$$ which gives $\%100$ of profit, How much does the fruit concentrate cost in $1$ liter of fruit juice? 

Let's recall $F =$ fruit concentrate cost, $W = $ Water cost and $P= $ packing cost,
$$W + F + \underbrace{P}_{0.32} = 1.2$$
Which yields
$$W + F = 0.88$$

Water cost equals $\%30$ of  fruit concentrate cost. 

$$W = \dfrac{30}{100}F$$
Then we have that
$$F + \dfrac{30}{100}F = 0.88 \implies F = 0.67692$$
I can't think of any way to proceed right now. 
Regards!
 A: If one liter of juice sells for $\$2.40$ at $100\%$ profit then the cost is $\$1.20$. Subtracting the $\$0.32$ cost of packaging, the concentrate and water costs $\$0.88$.
The water to concentrate cost ratio in the juice is $1:(\frac{20\%}{80\%}\cdot \frac{100\%}{30\%}) = 1:\frac{5}{6}$ or $6:5$
The water in one liter of juice costs $\frac{6}{11}\cdot 0.88 = 48$ cents 
The concentrate in one liter of juice costs $\frac{5}{11}\cdot 0.88 = 40$ cents
A: You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward.  I guess it means that the amount of fruit concentrate in the mixture is $25\%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.  
Let $x$ be the cost of a liter of fruit concentrate.  A liter of water costs $30\%$ of this or $.3x.$  Since we only have $20\%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$ 
Also, we have $80\%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$ 
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88\implies x=200\text{ cents}$$
EDIT
I misread the question.  I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture.  That's $20\%$ of $200$ cents or $40$ cents.
