Question $1$

a$)$ In the gear train shown in Figure $1,$ Shafts A and B are co$-$axial. Gear C has $50$ teeth and is rigidly mounted on shaft A $.$ Compound gear $\backslash (\backslash$mathrm$\{$D$\}-\backslash$mathrm$\{$E$\}\backslash )$ gears with C and an internal gear G $.$ Gear D has $20$ teeth and gears with C while gear E has $35$ teeth and gears with internal gear $\backslash ($ G $\backslash ).$

Gear G has $125$ external teeth, is concentric with the shaft axis and is driven by Gear H which has $40$ teeth. Compound gear D$-$E is mounted on a pin which projects from an arm keyed to the shaft B$.$ If Gear H rotates at $25$ rpm clockwise:

Find the number of internal teeth on Gear G and the speed of shaft B if Gear C is fixed $[6,14$ marks$]$