Question 41834
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 
{{{(0.2x + 0.7y)/(0.8x + 0.3y)}}}.
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, {{{(0.2x + 0.7y)/(0.8x + 0.3y)=7/13}}}
or {{{13(0.2x + 0.7y)=7(0.8x + 0.3y)}}}
or {{{2.6x + 9.1y=5.6x + 2.1y}}}
or {{{3x=7y}}}
or {{{x=7y/3}}} _________(1)


Again, the volume of the final solution is 20 litres.
So, {{{x + y = 20}}} ______(2)


Substituting for x from (1) in (2) we have
{{{7y/3 + y = 20}}}
or {{{10y/3 =20 }}}
or {{{y=20*3/10}}}
or y = 6
So {{{x = 7*6/3}}} = 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.