If [tex]c\%[/tex] is the unknown concentration of the second solution, then each mL of this solution that is used in the new one contributes [tex]0.01c[/tex] mL of acid.
There are 40 mL of the new solution, and one quarter is made up of 20% acid while the remaining three-quarters is made up of the [tex]c\%[/tex] solution - that is, 10 mL of a 20% acid solution are used, so that its contribution is 0.2(10 mL) = 2 mL of acid, while 30 mL of the [tex]c\%[/tex] solution are used, so it contributes [tex]0.01c(30\,\mathrm{mL})=0.3c\,\mathrm{mL}[/tex] of acid.
In this new solution, we want to get a concentration of 32% acid, so it should contain 0.32(40 mL) = 12.8 mL of acid. Then the total amount of acid in the new solution satisfies
[tex]0.3c+2=12.8\implies c=36[/tex]
so the second solution has a concentration of 36%. The equation used here is the same as the first choice (a),
[tex]30(0.36)+10(0.2)=40(0.32)[/tex]
