We know that the planets in the solar system orbit the sun in their elliptical paths. According to Kepler's third law on planetary motion
[tex](\frac{T_A}{T_B})^2=(\frac{r_A}{r_B})^3[/tex]
From equation (1), the period of revolution of Moon B is computed as:
[tex]\begin{gathered} T_B=(\frac{4r}{r})^{\frac{3}{2}}\cdot T_A \\ T_B=(4)^{\frac{3}{2}}20d \\ T_B=160\text{ days} \end{gathered}[/tex]
