An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

The correct answer is 375.

Let us break down the solution step-by-step by analyzing the gear system and their meshing relationships.

1. Given Data:
Number of teeth on sun gear A:
$T_A=20$
Number of teeth on planet gear B:
$T_B=30$
Number of teeth on the inner surface of gear C:
$T_{C,\text{in}}=80$
Number of teeth on the outer surface of gear C:
$T_{C,\text{out}}=100$
Number of teeth on external gear D:
$T_D=20$
Speed of sun gear A:
$N_A=300\text{rpm (clockwise)}$
Carrier arm AB is fixed:
$N_{\text{arm}}=0$
Let us assume the clockwise direction is positive (+) and the counter-clockwise direction is negative (-).

2. Speed of Planet Gear B:
Since sun gear A and planet gear B mesh externally, they rotate in opposite directions. The speed of gear B relative to gear A is given by:
$\frac{N_B}{N_A}=-\frac{T_A}{T_B}$
Substituting the given values:
$N_B=-300\times \frac{20}{30}=-200\text{rpm (counter-clockwise)}$

3. Speed of Ring Gear C:
Planet gear B meshes internally with the inner surface of gear C. For internal meshing, both gears rotate in the same direction:
$\frac{N_C}{N_B}=\frac{T_B}{T_{C,\text{in}}}$
Substituting the value of $N_B$:
$N_C=-200\times \frac{30}{80}=-75\text{rpm (counter-clockwise)}$

4. Speed of External Gear D:
The outer surface of gear C (with $T_{C,\text{out}}=100$ teeth) is part of the same rigid body C, meaning it rotates at the same speed:
$N_{C,\text{out}}=N_C=-75\text{rpm}$
The outer surface of gear C meshes externally with gear D. Therefore, their rotations are in opposite directions:
$\frac{N_D}{N_C}=-\frac{T_{C,\text{out}}}{T_D}$
Substituting the values:
$N_D=-\left(-75\right)\times \frac{100}{20}$
$N_D=75\times 5=375\text{rpm}$
Since the resulting speed is positive, gear D rotates in the clockwise direction.