In a real world circuit some portion of the circuit will be connected to the cabinet or other item the user can touch. It is always desirable to place the fuse in the power lead that is not so connected. That way when the fuse blows the absent minded human (who thinks that a blown fuse removes the power from the circuitry) can touch the circuitry without becoming part of the circuit.
Never make this assumption about disconnected power. Remove the primary power source by the line cord being removed from the wall outlet before opening the cabinet and touching the parts.
As they are designed the two circuits are fully isolated (the two returns are isolated). In this situation which fuse blows first is a matter of tolarances.
It will blow first the fuse that has the higher internal resistance and higher power dissipation
As the figur uses DC power source and
as the current direction is from positive to negative side, the fuse must be on the positive side. Regarding safety both in AC and DC sources fuse must be placed at the
first outlet point.
Im suggesting you that always use(learn first) some of not so complex technic for analysis ... Ist and IInd Kirhof rules ... its big step for begining but...
Most of simple cases have some trick, but in this case, only important thing:current it have same value in both cases... result its that both of fuses will be blow in same time ...