Excluding stoppages, the speed of a bus is 60 km/h. Including stoppages, its effective speed is 45 km/h. For how many minutes does the bus stop in each hour?

Introduction / Context:
This question is similar to an earlier stoppage problem and again examines how pauses affect the effective speed of a vehicle. The difference between the moving speed and the average speed tells us how much time is spent at rest. Understanding this relationship is valuable for interpreting timetables, planning trips and solving many standard aptitude problems where vehicles stop at intermediate stations.

Given Data / Assumptions:

Running speed of the bus (excluding stoppages) = 60 km/h.
Average speed including stoppages = 45 km/h.
We want to know how many minutes per hour the bus is not moving.
The bus is assumed to repeat a similar pattern each hour, with constant running speed when moving.

Concept / Approach:
As before, consider one hour of total clock time. At an effective speed of 45 km/h, the bus covers 45 km in that hour. If it travelled the same 45 km at its running speed of 60 km/h continuously, it would require less than one hour. The difference between one hour and the required moving time to cover 45 km at 60 km/h gives the stoppage time per hour. We apply time = distance / speed under both conditions using the same distance of 45 km.

Step-by-Step Solution:
Step 1: Assume reference distance based on effective speed. In 1 hour including stoppages at 45 km/h, the bus travels 45 km. Step 2: Compute moving time at 60 km/h for 45 km. time_moving = 45 / 60 hours. This simplifies to 3 / 4 hours. Step 3: Convert this moving time to minutes. (3 / 4) hours = (3 / 4) * 60 minutes = 45 minutes. Step 4: Find stoppage time per hour. Total time = 60 minutes, moving time = 45 minutes. Stoppage time = 60 - 45 = 15 minutes.

Verification / Alternative check:
If the bus runs 45 minutes at 60 km/h, it covers 60 * 45 / 60 = 45 km. Over the full 60 minutes, including 15 minutes of rest, the average speed is distance / time = 45 km / 1 hour = 45 km/h. This matches the given effective speed including stoppages, confirming that 15 minutes per hour is correct.

Why Other Options Are Wrong:
If stoppage time were 12 minutes, the bus would run for 48 minutes and cover 60 * 48 / 60 = 48 km in an hour, making the average speed 48 km/h, not 45 km/h. Similarly, 9 minutes or 10 minutes would also lead to incorrect effective speeds. Only 15 minutes of stoppage yields the specified 45 km/h effective speed from a running speed of 60 km/h.

Common Pitfalls:
Many candidates incorrectly try to adjust speed by a direct ratio, such as thinking that since 45 is three quarters of 60, stoppage time must be one quarter of an hour but then forgetting to convert that to minutes. That reasoning is actually correct here, but if applied carelessly in other contexts without checking distance and time, it can mislead. In all such problems, explicitly computing the time for a chosen distance using both speeds is the safest method.

Final Answer:
The bus stops for 15 minutes in every hour.