$A$ solid cylinder of length $\ell$ and cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\ell / 4$ in the denser liquid as shown in the figure. The lower density liquid has density $\varrho$ and the denser liquid has density $3\varrho$. The density $d$ of the solid cylinder is:

• A
  $\frac{1}{2} \varrho$
• B
  $\frac{3}{2} \varrho$
• C
  $\frac{3}{4} \varrho$
• D
  $\varrho$