Gearwheel A has 64 teeth. Gearwheel B has 40 teeth. Gearwheel C has 80 teeth. Gearwheel D has 32 teeth. Calculate the following: Torque on the shaft carrying gearwheel D.

Gear A and Gear B are meshing gears. The ratio of their rotational speeds is inversely proportional to the ratio of their number of teeth.
Given:
Rotational speed of gear A, $N_A = 800$ rpm
Number of teeth on gear A, $T_A = 64$
Number of teeth on gear B, $T_B = 40$

$$\frac{N_B}{N_A} = \frac{T_A}{T_B}$$ $$N_B = N_A \times \frac{T_A}{T_B}$$ $$N_B = 800\, \text{rpm} \times \frac{64}{40}$$ $$N_B = 800\, \text{rpm} \times 1.6$$ $$N_B = 1280\, \text{rpm}$$

Gears B and C are mounted on the same shaft, so they rotate at the same speed.

$$N_C = N_B$$ $$N_C = 1280\, \text{rpm}$$

Gear C and Gear D are meshing gears.
Given:
Number of teeth on gear C, $T_C = 80$
Number of teeth on gear D, $T_D = 32$

$$\frac{N_D}{N_C} = \frac{T_C}{T_D}$$ $$N_D = N_C \times \frac{T_C}{T_D}$$ $$N_D = 1280\, \text{rpm} \times \frac{80}{32}$$ $$N_D = 1280\, \text{rpm} \times 2.5$$ $$N_D = 3200\, \text{rpm}$$

The rotational speed of the shaft carrying gearwheel D is $\text{3200 rpm}$.