Answer:
120 liters of 60% alcohol solution is needed
Step-by-step explanation:
Let's assume
x liters of 60% alcohol solution is added
so, we get solution as
[tex]=\frac{60}{100}\times x[/tex]
[tex]=0.6x[/tex]
we are given
40 liters of a 20% alcohol solution is
[tex]=40\times\frac{20}{100}[/tex]
[tex]=40\times\frac{20}{100}[/tex]
[tex]=8[/tex]
so, total alcohol solution is
[tex]=8+0.6x[/tex]
now, we can find total solutions
total solutions is
[tex]=x+40[/tex]
now, it is making 50% solution
so, we get
[tex]\frac{8+0.6x}{x+40} =\frac{50}{100}[/tex]
now, we can solve for x
[tex]\left(8+0.6x\right)\cdot \:100=\left(x+40\right)\cdot \:50[/tex]
[tex]800+60x=50x+2000[/tex]
[tex]10x=1200[/tex]
[tex]x=120[/tex]
So,
120 liters of 60% alcohol solution is needed
