Question

How much 20% solution needs to be added to a 60% solution to make 400 ml of a 40% solution

Answer 1

Let $x$ be the volume of 20% solution, $y$ the volume of the 60% solution. We want a total volume of 400 mL in the final mixture, so

$x+y=400$

Each mL of either solution will contribute a corresponding concentration, and in the final mixture we want the 400 mL to have a 40% concentration, which means we should also have

$0.2x+0.6y=0.4\times400=160$

Solve the system and we get $x=y=200\,\rm{mL}$.