Question

The concentration of the mixture obtained by mixing two solutions, A and B, is 20%. The concentration of the second mixture obtained by mixing the same two solutions is 14.8%. Find the concentration of each of the solutions A and B, if the first mixture is obtained by mixing them in 1:1 ratio and the second is obtained by mixing them in 3:7 ratio.

Answer 1

Answer:

Concentration of solutions A and B are 33% and 7% respectively.

Step-by-step explanation:

Suppose, the concentration of solutions A and B are $x$ and $y$ respectively.

First mixture

Ratio of solutions A and B is 1 : 1

Lets assume the amount of solution A is $1v$ and amount of solution B is $1v$

Total amount of first mixture $=1v+1v=2v$ and concentration of first mixture is 20%

So, the first equation will be.......

$2v\times 0.20= (1v \times x)+(1v\times y)\\ \\ 0.40v=vx+vy\\ \\ x+y=0.40 .......................(1)$

Second mixture

Ratio of solutions A and B is 3 : 7

Lets assume the amount of solution A is $3v$ and amount of solution B is $7v$

Total amount of first mixture $=3v+7v=10v$ and concentration of first mixture is 14.8%

So, the second equation will be.......

$10v\times 0.148= (3v \times x)+(7v\times y)\\ \\ 1.48v=3vx+7vy\\ \\ 3x+7y=1.48 .......................(2)$

From equation (1), we will get :   $y=0.40-x$

Now substituting this $y=0.40-x$ into equation (2)......

$3x+7(0.40-x)=1.48\\ \\ 3x+2.80-7x=1.48\\ \\ -4x=1.48-2.80\\ \\ -4x=-1.32\\ \\ x=\frac{-1.32}{-4}=0.33$

Plugging this $x=0.33$ into equation (1), we will get......

$0.33+y= 0.40\\ \\ y=0.40-0.33=0.07$

So, the concentration of solution A is 0.33 or 33%  and the concentration of solution B is 0.07 or 7%