A compound gear train with gears $P$, $Q$, $R$ and $S$ has number of teeth $20$, $40$, $15$ and $20$, respectively. Gears $Q$ and $R$ are mounted on the same shaft as shown in the figure below. The diameter of the gear $Q$ is twice that of the gear $R$. If the module of the gear $R$ is $2$ $mm$, the center distance in $mm$ between gears $P$ and $S$ is
- $40$
- $80$
- $120$
- $160$