x = liters of 20% solution
Mixing the 20% solution with the 60 L of 90% solution gives a new mixture with volume (x + 60) L. Each L of the 20% solution contributes 0.2 L of alcohol and thus a total of 0.2x L of alcohol, while the 60 L of 90% solution contributes 54 L of alcohol.
We want the concentration of the new mixture to be 80%, so we require
[tex]\dfrac{0.2x+54}{x+60}=0.8[/tex]
Solve for x:
[tex]0.2x+54=0.8x+42[/tex]
[tex]12=0.4x[/tex]
[tex]\implies\boxed{x=30}[/tex]
So you will need 30 L of the 20% solution.
