Answer
The fraction of $q$ that ends up on sphere 1 is $~~\frac{1}{3}$
Work Step by Step
$V_1 = \frac{q_1}{4\pi~\epsilon_0~R_1}$
$V_2 = \frac{q_2}{4\pi~\epsilon_0~(2.00R_1)}$
Note that $V_1 = V_2$ and $q_2 = q-q_1$
We can find $q_1$:
$V_1 = V_2$
$\frac{q_1}{4\pi~\epsilon_0~R_1} = \frac{q_2}{4\pi~\epsilon_0~(2.00R_1)}$
$2.00~q_1 = q_2$
$2.00~q_1 = q-q_1$
$3.00~q_1=q$
$q_1= \frac{q}{3}$
The fraction of $q$ that ends up on sphere 1 is $~~\frac{1}{3}$.