How much pure water should be added to a 20% soap solution to make an 8% solution?
Let there was x amount of solution initially
so amount of soap in it is x/5
Let us add y amount of water to it
so
Percentage of soap is
$\displaystyle 8=\frac{x*100}{5 (x+y)}$
so
12x = 8y
3x=2y
so y= 2x/3
Which means 0.67 times the initial amount of solution