Question

How many liters of 60% alcohol solution should be added to 40 liters of a 20% alcohol solution to make a 50% solution?

Answer 1

120 liters of 60% alcohol solution is needed

Explanation:

Let's assume

x liters of 60% alcohol solution is added

so, we get solution as

`=(60)/(100)* x`

`=0.6x`

we are given

40 liters of a 20% alcohol solution is

`=40*(20)/(100)`

`=40*(20)/(100)`

`=8`

so, total alcohol solution is

`=8+0.6x`

now, we can find total solutions

total solutions is

`=x+40`

now, it is making 50% solution

so, we get

`(8+0.6x)/(x+40) =(50)/(100)`

now, we can solve for x

`\left(8+0.6x\right)\cdot \:100=\left(x+40\right)\cdot \:50`

`800+60x=50x+2000`

`10x=1200`

`x=120`

So,

120 liters of 60% alcohol solution is needed