Excluding stoppages, the speed of a bus is 72 km/h. Including stoppages, its effective speed becomes 60 km/h. For how many minutes does the bus stop in each hour?

Introduction / Context:
This question is about effective speed when a vehicle stops periodically. The difference between the running speed and the average speed including stoppages tells us how much time is spent stationary. Problems of this type are very common in time and distance and test whether a candidate can convert between speed and time using the same distance as a reference and correctly interpret a word description involving stoppages.

Given Data / Assumptions:

Running speed of the bus (when it is moving) = 72 km/h.
Average speed including stoppages = 60 km/h.
We need to find how many minutes per hour the bus remains stopped.
The bus is assumed to repeat a similar pattern of motion and stoppage every hour.

Concept / Approach:
Consider a period of one hour of clock time. At the effective average speed of 60 km/h, the bus covers 60 km in that one hour. If it were to travel continuously at its running speed of 72 km/h without any stop, it would take less than one hour to cover 60 km. The difference between one hour and that smaller travel time is exactly the stoppage time within the hour. We use time = distance / speed with the same distance (60 km) for both running and effective conditions.

Step-by-Step Solution:
Step 1: Assume a reference distance. In one hour including stoppages, at 60 km/h, the bus covers 60 km. Step 2: Compute the moving time needed to cover 60 km at 72 km/h. time_moving = 60 / 72 hours. Simplify: 60 / 72 = 5 / 6 hours. Step 3: Convert moving time into minutes. (5 / 6) hours = (5 / 6) * 60 minutes = 50 minutes. Step 4: Find stoppage time per hour. Total clock time = 60 minutes, moving time = 50 minutes. Stoppage time = 60 - 50 = 10 minutes.

Verification / Alternative check:
If the bus runs 50 minutes at 72 km/h, the distance covered is (72 * 50 / 60) = 60 km. Over the full 60 minutes, including the 10 minutes of stoppage, the average speed is distance / time = 60 km / 1 hour = 60 km/h. This matches the given effective speed, confirming that 10 minutes per hour of stoppage is correct.

Why Other Options Are Wrong:
If stoppage time were 12 minutes, the bus would only run for 48 minutes, covering 72 * 48 / 60 = 57.6 km, giving an effective speed of 57.6 km/h, not 60 km/h. Similar mismatches occur with 8 or 15 minutes. Only a 10 minute stoppage yields an effective 60 km/h from a running speed of 72 km/h with the same one hour period.

Common Pitfalls:
Some students mistakenly compare 72 and 60 directly and try to work with a ratio of speeds without fixing a reference distance or time. Others compute how much distance is lost instead of time lost, which can be confusing. The safest approach is to pick a convenient distance based on effective speed in exactly one hour, then recompute the time needed at the running speed and subtract to find stoppage time.

Final Answer:
The bus stops for 10 minutes in every hour.