percentage problem in solution

Question

I have solve this percentage problem by back solving method. Can't I solve this straight forwardly and easy way?

Answer 1

Let ratio of $20\%:50\%$ be $1:x$ then, $$ \frac{20\% + x 50\%}{1 + x} = 40 \% $$ that gives $x=2$.

Answer 2

For a hand-waving solution: The $40\%$ solution she wants is $\frac{2}{3}$ of the way from the "weak" $20\%$ stock solution to the "strong" $50\%$ stock solution, so she needs $\frac{2}{3}$ strong and $\frac{1}{3}$ weak...