A man travels from his village to the post office at 25 km/h and then walks back from the post office to the village at 4 km/h. If the total time for the journey to and from the post office is 5 hours 48 minutes, what is the distance between the village and the post office?

Introduction / Context:
This is a round trip time and distance problem with different speeds in the two directions. The total time for going and returning is given, and we must find the one way distance. These types of questions are common in aptitude tests and require setting up a clear equation using the basic formula distance = speed * time.

Given Data / Assumptions:

- Speed from village to post office = 25 km/h.
- Speed from post office back to village = 4 km/h.
- Total time for the complete journey = 5 hours 48 minutes.
- One way distance between village and post office = D km (unknown).
- Motion is in a straight line with constant speeds in each direction.

Concept / Approach:
We treat the outward and return journeys separately, writing each travel time as distance divided by speed. The sum of these two travel times is given as 5 hours 48 minutes. Converting minutes to hours and solving the resulting equation gives the one way distance D. This is a straightforward application of algebra and unit conversion.

Step-by-Step Solution:
Let the distance between village and post office be D km. Time from village to post office = D / 25 hours. Time from post office back to village = D / 4 hours. Total time = D / 25 + D / 4 hours. Given total time = 5 hours 48 minutes = 5 + 48 / 60 = 5.8 hours. So we have D / 25 + D / 4 = 5.8. Take common denominator 100: (4D + 25D) / 100 = 5.8. So 29D / 100 = 5.8. Therefore D = 5.8 * 100 / 29 = 20 km.

Verification / Alternative check:
Using D = 20 km, time outward at 25 km/h = 20 / 25 = 0.8 hours (48 minutes). Time return at 4 km/h = 20 / 4 = 5 hours. Total time = 5 + 0.8 = 5.8 hours, which is 5 hours 48 minutes. This matches the given total time exactly, confirming that D = 20 km is correct.

Why Other Options Are Wrong:
40 km, 30 km, and 10 km: Substituting any of these into the expressions for travel times will not give a total of 5 hours 48 minutes. For example, 40 km would already take 10 hours on the return trip alone at 4 km/h, which is too large.

Common Pitfalls:
Students sometimes average the two speeds and multiply by half the total time, which is incorrect because the times in each direction are not equal. Others forget to convert 48 minutes into 0.8 hours, leading to wrong numerical results. Always treat each direction separately and add the times after converting all units consistently.

Final Answer:
The distance between the village and the post office is 20 km.