Question

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A. 10
B. 9
C. 8
D. 7

Answer 1

Hint: Calculate the distance travelled by bus in 1 hour excluding stoppages. Then calculate the distance travelled by bus in 1 hour including stoppages.
After this find the difference between the distances travelled including and excluding the stoppages. Then calculate the time taken to cover that “difference of the distances calculated above” and convert the calculated time into minutes.

Complete step-by-step answer:

It is given that, excluding stoppages, the speed of a bus is 54 kmph.
$\Rightarrow $ Distance travelled by bus in 1 hour, excluding stoppages = 54 km.
Also, it is given that including stoppages the speed of the bus is 45 km/hr.
$\Rightarrow $ Distance travelled by the bus in 1 hour, including stoppages = 45 km.
(Distance travelled by bus in 1 hour excluding stoppages – distance travelled by bus in 1 hour including stoppages)
\[\begin{align}
  & \Rightarrow \left( 54km-45km \right) \\
 & \Rightarrow 9km \\
\end{align}\]
That means, due to stoppages, the bus covers 9 km less.
Hence, time taken to cover 9 km,
$=\dfrac{\text{distance travelled}}{\text{speed of the bus}}$
It is given usual speed of the bus = 54 km/hour
$\therefore $ Time taken to cover 9 km $=\dfrac{9km}{54km/hour}$
$=\dfrac{1}{6}hour$
Time taken in minutes $=\left( \dfrac{1}{6}\times 60 \right)\text{minutes}$
$\text{=10minutes}$
(Since, 1 hour = 60 minutes)
Therefore, the bus stops per hour for 10 minutes.
Hence, option A is correct.

Note: Students can easily solve this question by using this trick.
Required time for the stoppage per hour,
$\begin{align}
  & =\dfrac{\text{difference of speeds}}{\text{speed without stoppage}} \\
 & =\left( \dfrac{54-45}{54} \right)hour \\
 & \Rightarrow \dfrac{9}{54}=\dfrac{1}{6} \\
 & =\left( \dfrac{1}{6}\times 60 \right)\text{minutes} \\
 & \left( \text{since 1 hour = 60 minutes} \right) \\
 & \text{=10minutes} \\
\end{align}$