$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$, cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid (density $2d$) and $3L/4$ in the lighter liquid (density $d$). The lower density liquid is open to the atmosphere having pressure $P_0$. Then, the density $D$ of the solid is given by:

• A
  $\frac{5}{4}d$
• B
  $\frac{4}{5}d$
• C
  $4d$
• D
  $\frac{d}{5}$