Question

Excluding stoppages the speed of a bus $54\dfrac{km}{hr}$ and including stoppage it is $45\dfrac{km}{hr}$ . For how long does the bus stop per hour?
A) 9 min
B) 15 min
C) 12 min
D) 10 min

Answer 1

Hint: We have 2 speeds of a bus. One is excluding stoppages and other is including stoppages, So, we can calculate distance per hour with and without stoppages. So, from that we can set the difference of distances when stoppages are there and also when stoppages are not there, So, we can calculate the time taken from this difference as we already know the speed of the bus without stoppages. This will be the time of stopping the bus per hour as at first, we took distance travelled per hour. By general basic knowledge of physics, we can say the formula of speed to be given by:
$\text{Speed}\ \text{=}\ \dfrac{\text{Distance travelled}}{\text{time taken}}$
Complete step-by-step answer:
Distance travelled by bus while we include that the bus will never stop at any point:
Given speed in this case, is speed without any stoppages $=\ 54\ kmph$
If we take time as 1 hour, the distance travelled will be:
$\text{distance travelled}\ \text{= speed}\times \text{time}=\ 54\times 1\ =\ 54$
The distance travelled by bus while we include that the bus will never stop at any point $=\ 54\ km$
Distance travelled by bus, while we include that the bus will stop at given stoppages:
Speed of bus with stoppages, is given in question as:
$=\ 45\ kmph$
If we take time as 1 hour, distance travelled will be:
$=\ 45\ \times 1\ =\ 45\ km$.
Distance travelled by bus, while we include that the bus will stop at given stoppages per hour $=\ 45\ km$
Difference in the distances $=\ 54-\ 45\ =\ 9\ km$
As we know without any stoppages the speed of bus: $=\ 54\ kmph$
So, the difference being the distance we will know that the bus stops per hour.
$\text{time}\ \text{=}\ \dfrac{\text{Distance }}{\text{speed}}\ =\ \dfrac{9}{54}\ hr$
$1\ \text{hour}\ \text{=}\ \text{60}\ \text{min}$. By using this condition, we get $\text{time}\ =\ \left( \dfrac{9}{54}\times 60 \right)\ \min \ =\ 10\min $.
Thus, we say bus stops for 10 min per hour. Hence, option (D) is the correct answer.

Note: Be careful while calculating the speed in both times as it varies from time to time. We take $\text{time}\ =\ 1\ \text{hour}$ as in the question they asked distance, bus stops per hour.