SOLUTION: how many liter of 20% solution and 70% solution do you need to make 20 liter of a 35% solution.

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Question 41834: how many liter of 20% solution and 70% solution do you need to make 20 liter of a 35% solution.
Answer by psbhowmick(878) (Show Source):
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20% solution and 70% solution means that the ratio of solute to solvent by volume is 20:80 i.e. 1:4 and 70:30 i.e. 7:3 respectively.

Let us suppose that 'x' litres of the 20% solution is mixed with 'y' litres of the 70% solution to produce 20 litres of 35% solution.

Then, volume of solute added from 20% solution = 0.2x litres
and volume of solute added from 70% solution = 0.7y litres
Thus total volume of solute in the final solution = (0.2x + 0.7y) litres.

Then, volume of solvent added from 20% solution = 0.8x litres
and volume of solvent added from 70% solution = 0.3y litres
Thus total volume of solvent in the final solution = (0.8x + 0.3y) litres.

Hence the ratio of solute to solvent by volume in the final solution is
.
As the final solution is 35% so the ratio of solute to solvent by volume in the final solution is 35:65 i.e. 7:13.
So,
or
or
or
or _________(1)

Again, the volume of the final solution is 20 litres.
So, ______(2)

Substituting for x from (1) in (2) we have

or
or
or y = 6
So = 14

Hence 14 litres of the 20% solution has to be mixed with 6 litres of the 70% solution to yield 20 litres of 35% solution.