After excluding stoppages, the speed of a bus is 60 km/h, but including stoppages its average speed falls to 45 km/h. For how many minutes per hour does the bus stop?

Introduction / Context:
This question combines average speed with the idea of stoppage time. It tests whether you understand how halts affect the effective average speed of a vehicle and how to convert between hours and minutes while handling distances. The concept appears often in time, speed, and distance sections of aptitude exams.

Given Data / Assumptions:
- Actual running speed when the bus is moving = 60 km/h.
- Average speed including stoppages = 45 km/h.
- Time considered = 1 hour of clock time (for convenience).
- Let running time in that hour be t hours and stoppage time be s hours, with t + s = 1.
- Distance covered in the hour is 45 km (since average speed is 45 km/h for 1 hour).

Concept / Approach:
If we know the effective average speed over one hour, we can find the distance covered in that hour. That distance must also equal the running speed multiplied by the actual running time, because no distance is covered during stoppages. By equating 60 * t to 45, we can find t. Then, stoppage time s is simply 1 - t. Finally, convert s from hours into minutes.

Step-by-Step Solution:
Step 1: Distance covered in one hour of clock time at an average of 45 km/h is 45 km.Step 2: Let the bus actually runs for t hours at 60 km/h during this period.Step 3: Distance covered while running = 60 * t km.Step 4: This distance must equal 45 km, so 60 * t = 45.Step 5: Solve for t: t = 45 / 60 = 3 / 4 hours.Step 6: Stoppage time per hour s = 1 - t = 1 - 3 / 4 = 1 / 4 hour.Step 7: Convert 1 / 4 hour to minutes: (1 / 4) * 60 = 15 minutes.

Verification / Alternative check:
Check by recomputing the average speed from these times. In one hour, the bus runs for 45 minutes at 60 km/h. Distance covered = 60 * (45 / 60) = 45 km. Average speed = total distance / total time = 45 km / 1 hour = 45 km/h, which matches the given information. Therefore 15 minutes stoppage per hour is consistent.

Why Other Options Are Wrong:
- 10, 9, and 12 minutes would correspond to different effective average speeds; substituting them into the calculation would not yield 45 km/h as the combined average speed.

Common Pitfalls:
Some students incorrectly assume that average speed is the arithmetic mean of 60 km/h and 0, which would be 30 km/h, not 45 km/h. Another mistake is to forget that average speed equals total distance divided by total time, not simply an average of speeds. Also, ensure that you use the same time unit (hours or minutes) consistently in the calculation and only convert at the end.

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