>Do not remember why a double gear reduction is need?
Too fast a motor? Too low power (or Torque)?
How to calculate the ratio when double gear?<

James answered this from a toothed gear point of you and it applies similarly to a belt drive.  The double gear reduction is get a better ratio without having a huge pulley on the pump.  It keeps the pump "package" smaller and the pump itself can be mounted lower.  Gearboxes are expensive, I am assuming Maxant is using the the jackshaft pulley setup to bring the overall cost down.  As far as calculation the ratio with the jackshaft, simply multiply the ratio's together.

(Motor Driven/Output)*(Jackshaft Driven/Pump Output)=Overall reduction

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