Excluding stoppages, the average speed of a bus is 60 km/h. Including stoppages, the average speed drops to 40 km/h. For how many minutes per hour does the bus stop?

Introduction / Context:
This question is about effective average speed when a vehicle stops intermittently. It checks understanding that average speed including stoppages is lower than the running speed and that the difference arises from time spent not moving. The problem asks you to interpret average speed values to compute total stoppage time in one hour of the schedule.

Given Data / Assumptions:

• Running average speed without stoppages = 60 km/h.
• Overall average speed including stoppages = 40 km/h.
• We consider a 1 hour schedule (60 minutes).
• The bus either moves at 60 km/h or is stopped; there are no other speeds.

Concept / Approach:
In one hour of clock time, the bus covers 40 km on average. When it is moving at 60 km/h, the distance covered in the moving time is 60 * T hours, where T is the time in motion. Since this must equal 40 km, we solve 60 * T = 40 to find the moving time. The stoppage time is the remainder of the hour.

Step-by-Step Solution:
Let T be the time (in hours) for which the bus is moving in one hour of schedule. Distance covered while moving: 60 * T km. Overall average is 40 km/h, so in one hour the bus covers 40 km. Equate the distances: 60 * T = 40. So T = 40 / 60 = 2 / 3 hour. Total time in one hour = 1 hour. Stoppage time = 1 - 2 / 3 = 1 / 3 hour. Convert 1 / 3 hour to minutes: (1 / 3) * 60 = 20 minutes.

Verification / Alternative check:
If the bus moves 40 minutes at 60 km/h, distance covered is 60 * (40 / 60) = 40 km. For the remaining 20 minutes it stands still. Total time is 60 minutes, total distance is 40 km, so the overall average speed is 40 km/h, exactly as given.

Why Other Options Are Wrong:

• 2 minutes, 30 minutes and 40 minutes do not satisfy the equation 60 * T = 40 when converted back to hours and tested.

Common Pitfalls:
Students sometimes try to use ratios of speeds directly without interpreting them as distances over time. Another common mistake is to assume linear proportionality between speed and stoppage time without forming an equation. Carefully equating the distance from the running speed with the distance from overall average speed avoids these errors.

Final Answer:
The bus stops for 20 minutes in every hour of its schedule.