A bus has a running speed of 80 km/h when it is moving without any stops. Including regular stoppages, its average speed over the whole hour reduces to 60 km/h. For how many minutes in each hour does the bus remain stopped?

Introduction / Context:
This problem examines the difference between running speed and average speed when stoppages are involved. It is a common type of question in time and distance where one must determine how long a vehicle is stationary based on its effective speed across a full hour. The concept closely relates to practical travel planning and timetable analysis.

Given Data / Assumptions:

Running speed of the bus when it is moving = 80 km/h.
Average speed including stoppages = 60 km/h.
The time interval considered is 1 hour, that is 60 minutes.
When the bus is stopped, it covers no distance.
Speeds are assumed constant while the bus is in motion.

Concept / Approach:
Average speed is defined as total distance divided by total time taken, including both running time and stoppage time. In one hour, at an average speed of 60 km/h, the bus covers a distance of 60 km. However, whenever it is moving, it does so at 80 km/h. Hence, we first compute how much running time is needed to cover 60 km at 80 km/h. The remaining fraction of the hour is the stoppage time. Converting that fraction into minutes gives the required answer.

Step-by-Step Solution:
Step 1: In one hour, at an average speed of 60 km/h, the bus covers 60 km. Step 2: Let the time in hours for which the bus is actually moving be t hours. While running, its speed is 80 km/h. Step 3: Distance covered during running is 80 * t kilometres. This must be equal to the total distance of 60 km, so 80 * t = 60. Step 4: Solve for t: t = 60 / 80 = 3 / 4 hour = 0.75 hour. Step 5: Total time in an hour is 1 hour, so stoppage time = 1 − 0.75 = 0.25 hour. Step 6: Convert 0.25 hour into minutes: 0.25 * 60 = 15 minutes.

Verification / Alternative check:
If the bus runs for 45 minutes and stops for 15 minutes, in 45 minutes (which is 0.75 hour) at 80 km/h it travels 80 * 0.75 = 60 km. Over the full hour, distance is 60 km and time is 1 hour, so average speed is 60 km/h, which matches the given value. This confirms that the stoppage time of 15 minutes per hour is correct.

Why Other Options Are Wrong:
A stoppage time of 12 minutes or 10 minutes would give more running time and therefore a higher effective average speed than 60 km/h. Stoppages of 18 or 20 minutes would reduce the distance covered in an hour below 60 km at a running speed of 80 km/h, giving a lower average speed. Only 15 minutes of stoppage yields exactly the required average speed of 60 km/h.

Common Pitfalls:
Learners sometimes confuse running speed and average speed and try to subtract speeds directly, which is incorrect. Another error is assuming that the average speed is simply the mean of two speeds, which does not hold when there are periods of rest. Correctly defining distance covered during the running time and dividing by the total time, including stops, is essential for solving such problems accurately.

Final Answer:
The bus stops for 15 minutes per hour.