Question 52078
Let x = the number of liters of the 10% alcohol solution.
From the problem description, you can write the equation: (Note:  Change the percents to their decimal equivalents) The final solution will be (40+x) liters.
{{{x(0.1) + 40(0.5) = (40+x)(0.4)}}} Simplify and solve for x.
{{{0.1x + 20 = 16 + 0.4x}}} Subtract 0.1x from both sides of the equation.
{{{20 = 16 + 0.3x}}} Subtract 16 from both sides.
{{{4 = 0.3x}}} Finally, divide both sides by 0.3
{{{13.33 = x}}}

You will need to mix 13.33...(or 13 1/3) liters of 10% alcohol solution with 40 liters of 50% alcohol solution to obtain 53.33... (or 53 1/3) liters of 40% alcohol solution.

Check:
13.33(0.1) + 40(0.5) = 53.33(0.4)
1.333 + 20 = 21.333
21.333 = 21.333