SOLUTION:
The helpful formula or guide is given thus;
[tex]\frac{N_1}{N_2}\text{ = }\frac{T_2}{T_1}[/tex]Where N represents the number of teeth on gear and T represents RPM of gear.
(a)
[tex]\begin{gathered} \frac{20}{48}\text{ = }\frac{x}{240} \\ 48\text{ x = 20 X 240} \\ 48x\text{ = }4800 \\ x\text{ = }\frac{4800}{48} \\ x\text{ = }100 \end{gathered}[/tex](b)
[tex]\begin{gathered} \frac{25}{x}\text{ = }\frac{420}{150} \\ 420x\text{ = 25 x 150} \\ 420x\text{ = 3750} \\ x\text{ = }\frac{3750}{420} \\ x\text{ = 8.9286} \\ x\text{ = 9} \end{gathered}[/tex](c)
[tex]\begin{gathered} \frac{x}{40}\text{ = }\frac{100}{160} \\ 160x\text{ = 40 x 100} \\ 160x\text{ = 4000} \\ x\text{ = }\frac{4000}{160} \\ x\text{ = 25} \end{gathered}[/tex](d)
[tex]\begin{gathered} \frac{32}{40}\text{ = }\frac{1200}{x} \\ 32x\text{ = 40 x 1200} \\ 32x\text{ = 48000} \\ x\text{ = }\frac{48000}{32} \\ x\text{ = 1500} \end{gathered}[/tex]