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*400=160`

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