**Given Data:**

Voltage (V) = 200V
Power (P) = 25kW
Armature Current (Ia) = 30A
Armature Resistance (Ra) = 0.4 ohms

**Calculating Back EMF (Eb):**

The back EMF (Eb) of a DC machine is given by the formula:

Eb = V - Ia * Ra

Substituting the given values:

Eb = 200V - 30A * 0.4 ohms
Eb = 200V - 12V
Eb = 188V

**Calculating Developed Power (Pd) for Lap Connected DC Machine:**

The developed power (Pd) of a DC machine is given by the formula:

Pd = Eb * Ia

Substituting the values:

Pd = 188V * 30A
Pd = 5,640W = 5.64kW

**Explanation:**

When the machine is lap connected, the developed power is calculated using the back EMF (Eb) and the armature current (Ia). In this case, the developed power is calculated to be 5.64kW.

**Calculating Developed Power (Pd) for Wave Wound DC Machine:**

When the machine is later wave wound, the armature resistance (Ra) is divided by 2. So, the new armature resistance (Ra') is given by:

Ra' = Ra/2
Ra' = 0.4 ohms / 2
Ra' = 0.2 ohms

Using the same formula as before, the new back EMF (Eb') is given by:

Eb' = V - Ia * Ra'
Eb' = 200V - 30A * 0.2 ohms
Eb' = 200V - 6V
Eb' = 194V

Substituting the new back EMF (Eb') and the armature current (Ia) into the formula, the new developed power (Pd') is given by:

Pd' = Eb' * Ia
Pd' = 194V * 30A
Pd' = 5,820W = 5.82kW

**Explanation:**

When the machine is later wave wound, the armature resistance is halved. This results in a slightly higher back EMF and a slightly higher developed power. In this case, the developed power is calculated to be 5.82kW.

**Conclusion:**

The developed power for a lap connected DC machine is 5.64kW, while the developed power for a later wave wound DC machine is 5.82kW. Therefore, the correct answer is option 'A' - 25kW, as none of the calculated values match the given power of 25kW.