Let's analyze the problem in the image.

Problem:

• We can complete a job in 30 days with p machines.
• With (p + 4) machines, a job with double the difficulty takes 40 days.
• The question asks: How long will it take for (p + 2) machines to complete a job of the same difficulty as the original?

Step-by-Step Solution:

1. Work Rate of p Machines: If p machines can complete a job in 30 days, the total work can be defined as: $\text{Work} = p \times 30$ Thus, the work rate of p machines is: $\text{Rate of p machines} = \frac{1}{30} \text{ (jobs/day)}$

2. Work Rate of (p + 4) Machines: With (p + 4) machines, the job is twice as difficult and takes 40 days. This means that the amount of work is doubled. The total work is now: $2 \times (\text{Work}) = 2p \times 30$ The rate of (p + 4) machines can be expressed as: $\frac{p + 4}{40} = \frac{2p}{30}$

3. Solving for p: We now solve the equation: $\frac{p + 4}{40} = \frac{2p}{30}$ Cross-multiplying: $30(p + 4) = 80p$ Simplifying: $30p + 120 = 80p$ $120 = 50p$ $p = \frac{120}{50} = 2.4$

4. Time for (p + 2) Machines: Now that we know p = 2.4, we calculate how long it will take for (p + 2) machines to complete the original job. With (p + 2) = 4.4 machines, the rate is: $\text{Rate of } (p + 2) \text{ machines} = \frac{4.4}{T}$ This rate should equal the rate for the original job: $\frac{4.4}{T} = \frac{2.4}{30}$ Solving for T: $4.4 \times 30 = 2.4 \times T$ $132 = 2.4 \times T$ $T = \frac{132}{2.4} = 55 \text{ days}$

Thus, the correct answer is 55 days, but it seems the problem might not have been correctly translated into the options provided. Let's reconsider any details or adjustments if needed.