To obtain 50 liters of a 13% sugar solution, mix some 25% and some 10% sugar solution.

To obtain 50 liters of a 13% sugar solution, mix some 25% and some 10% sugar solution. How many liters of each solution should you take?

1. The volume of the resulting solution: V13 = 50 l;

2. The volume of the solution with a concentration of 10%: V10 l;

3. The volume of a solution of 25% concentration: V25 l;

4. First equation;

V25 + V10 = V13 = 50 l;

5. Let us express: V10 = (50 – V25) l;

6. Composing the sugar balance:

0.25 * V25 + 0.1 * V10 = 0.13 * V13;

0.25 * V25 + 0.1 * (50 – V0.25) = 0.13 * 50;

0.15 * V25 = 6.5 – 5 = 1.5;

7. Determine the volumes of solutions:

V25 = 1.5 / 0.15 = 10 l;

V10 = V13 – V25 = 50 – 10 = 40 HP

Answer: you need to take 10 liters of a 25% solution and 40 liters of a 10% sugar solution.