Question

The speed of a bus is 54 km/hr excluding stoppage and 45 km/hr including stoppages. For how many minutes does the bus stop per hour?
A.12 min
B.10 min
C.8 min
D.6 min

Answer 1

Hint: The bus will cover more distance when travelling at a speed of 54 km/hr than at a speed of 45 km/hr. First, we subtract both the given speeds to find the extra distance travelled when the bus travels at a speed of 54 km/hr. The time taken to cover that distance is calculated using the following formula for time,
\[\text{time}=\dfrac{\text{distance}}{\text{speed}}\]
The time will be calculated in hours. We will have to convert it to minutes by multiplying it with 60.

Complete step-by-step answer:
Since speed decreases from 54 km/hr to 45 km/hr, loss in speed is calculated as:
\[54-45=9\text{ km/hr}\]
Therefore, we can say that the bus covers 9 km less in 1 hour when speed is reduced. Time taken to cover this distance is calculated as:
  $ \text{time}=\dfrac{\text{distance}}{\text{speed}} $
 $ \text{ }=\dfrac{9\text{ km}}{54\text{ km/hr}} $
 $ \text{ }=\dfrac{1}{6}\text{ hr} $
To convert into minutes, we multiply by 60 as follows:
\[\dfrac{1}{6}\times 60=10\text{ min}\]
Therefore, the bus stops for 10 min per hour.
So, the correct answer is “Option B”.

Note: Since the original speed of the bus is 54 km/hr, we have to substitute this value in the formula to find time. Since the options are in minutes, we should not forget to convert to minutes. The formula for time can be derived from the formula for speed, that is, \[\text{speed}=\text{distance/time}\].