A certain amount of water was added to a 30% alcohol solution and a 10% solution was obtained. How much water was added?

1. To reduce the concentration of the solution by 3 times, you need to increase the volume of the solution by 3 times by adding water.

2. Let us prove. Let at the beginning X be the volume of water, Y – the volume of alcohol. Then Y = 0.3 (X + Y). (30% solution).

3. Add Z water (Z – volume). We get Y = 0.1 (X + Y + Z). (10% solution).

4. We get the equation: 0.3 (X + Y) = 0.1 (X + Y) + 0.1 Z.

5. Solution: Z = 2 (X + Y), that is, the volume of added water Z is twice the original volume of the solution (X + Y).