**Understanding the Problem:**
We are given two speeds of a bus - 54 km/h excluding stoppages and 45 km/h including stoppages. We need to find out how many minutes the bus stops per hour.

**Solution:**

To find the amount of time the bus stops per hour, we need to calculate the difference in time between the two speeds.

Let's assume that the bus travels for 'x' minutes without stopping.

The distance covered by the bus in 'x' minutes at a speed of 54 km/h can be calculated using the formula:
Distance = Speed × Time
Distance = 54 km/h × (x/60) h
Distance = 54x/60 km

Similarly, the distance covered by the bus in 'x' minutes at a speed of 45 km/h can be calculated using the formula:
Distance = Speed × Time
Distance = 45 km/h × (x/60) h
Distance = 45x/60 km

Now, we know that the distance covered by the bus without stoppages is the same as the distance covered by the bus with stoppages.

Therefore, we can equate the two distances:

54x/60 = 45x/60

Simplifying the equation, we get:

54x = 45x

9x = 0

Since the equation 9x = 0 has no solutions other than x = 0, this means that the bus does not stop at all.

Hence, the bus does not stop per hour.

**Conclusion:**
Based on the given information, the bus does not stop per hour.