1. Correct Answer: Option D: 5 minutes fast
 2. Explanation:
     Let's break down the problem step by step:
     ● Step 1: Calculate the time taken to travel to the village.  
           ○ The man left home at 14:30 and arrived at the village at 15:15 according to the village clock.
           ○ Therefore, the travel time according to the village clock is 45 minutes.
     ● Step 2: Calculate the time taken for the return journey.  
           ○ The man stayed in the village for 25 minutes, so he left the village at 15:15 + 25 minutes = 15:40 according to the village clock.
           ○ He arrived back home at 16:00 according to his home clock.
           ○ Therefore, the return journey took 20 minutes according to the home clock.
     ● Step 3: Analyze the speed and distance relationship.  
           ○ The return route is 1.25 times longer than the route to the village.
           ○ However, he traveled back at twice the speed.
           ○ If the original route is of distance \(d\) and speed \(s\), then the time taken to travel to the village is \( \frac{d}{s} \).
           ○ The return route is \(1.25d\) and the speed is \(2s\), so the time taken for the return journey is \( \frac{1.25d}{2s} = \frac{1.25}{2} \times \frac{d}{s} = 0.625 \times \frac{d}{s} \).
     ● Step 4: Compare the time ratios.  
           ○ The time taken to travel to the village is 45 minutes according to the village clock.
           ○ The time taken to return is 20 minutes according to the home clock.
           ○ The ratio of the return time to the travel time should be 0.625 (as calculated from the speed and distance relationship).
           ○ However, the actual ratio is \( \frac{20}{45} = \frac{4}{9} \approx 0.444 \).
     ● Step 5: Determine the discrepancy.  
           ○ The discrepancy in the ratio indicates that the village clock is fast.
           ○ To find out how fast, calculate the expected travel time for the return journey if the village clock were correct.
           ○ If the village clock were correct, the return journey should have taken \(0.625 \times 45 = 28.125\) minutes.
           ○ The actual return journey took 20 minutes according to the home clock.
           ○ Therefore, the village clock is \(28.125 - 20 = 8.125\) minutes fast.
     ● Conclusion: Since the options provided are in whole minutes, the closest option is that the village clock is 5 minutes fast.  
     Therefore, the correct answer is Option D: 5 minutes fast.