Answer
$\frac{d_A}{d_B} = 0.25$
Work Step by Step
It is given that the cylinders originally had the same length. Since the bricks is horizontal, the cylinders must have the same length when they are supporting the brick. Thus $~~strain = \frac{\Delta L}{L}~~$ is equal for both cylinders.
We can find the relationship between the forces on each cylinder:
$\frac{\Delta L}{L} = \frac{F_A}{A_A~E_B} = \frac{F_B}{A_B~E_B}$
$F_A = \frac{A_A~E_A}{A_B~E_B}~F_B$
$F_A = \frac{(2~A_B)~(2~E_B)}{A_B~E_B}~F_B$
$F_A = 4~F_B$
To find the ratio of $\frac{d_A}{d_B}$, we can consider the torque about the center of mass:
$d_A~F_A = d_b~F_B$
$\frac{d_A}{d_B} = \frac{F_B}{F_A}$
$\frac{d_A}{d_B} = \frac{F_B}{4~F_B}$
$\frac{d_A}{d_B} = \frac{1}{4}$
$\frac{d_A}{d_B} = 0.25$
