Question & Answer
QUESTION

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75kms away from point A at the same time. On the way however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is
a)100kmph
b)110kmph
c)120kmph
d)130kmph

ANSWER Verified Verified
Hint: We need to use the speed distance formula to solve this question. We can take the speed of the car as a variable and use the information given in the question to obtain the corresponding equations and then solve for this variable.

Complete step-by-step answer:
Let the speed of the car be ${{v}_{c}}$. As it is given in the question that the train can travel 50% faster than the car, the speed of the train ${{v}_{t}}$ would be given by
${{v}_{t}}={{v}_{c}}+\dfrac{50}{100}{{v}_{c}}=\dfrac{3}{2}{{v}_{c}}..............(1.1)$
In the question, it is given that the distance travelled by both the train and the car from point A to point B = 75km.
We use the time-speed relation which states that
$\text{time taken=}\dfrac{\text{distance}}{\text{speed}}$
Thus, time taken by the car to reach point B is
${{t}_{c}}=\dfrac{75}{{{v}_{c}}}...................(1.2)$
However, the train loses 12.5 minutes while stopping at the stations, we know that
$\text{time in hours=}\dfrac{\text{time in minutes}}{60}$
Therefore, time lost by the train is
$\text{time lost by train=}\dfrac{12.5}{60}hours............(1.3)$
Thus, time taken by the train to reach point B (by using equation 1.1 and 1.3) is
${{t}_{t}}=\text{time lost by train+}\dfrac{75}{{{v}_{t}}}=\dfrac{12.5}{60}\text{+}\dfrac{75}{\dfrac{3}{2}{{v}_{c}}}...................(1.4)$
As, it is given that the time taken by the train and the car are same, we can equate (1.2) and (1.4) to obtain
$\begin{align}
  & \dfrac{75}{{{v}_{c}}}=\dfrac{12.5}{60}\text{+}\dfrac{75}{\dfrac{3}{2}{{v}_{c}}} \\
 & \Rightarrow \dfrac{75}{{{v}_{c}}}-\dfrac{2\times 75}{3{{v}_{c}}}=\dfrac{12.5}{60}\Rightarrow \dfrac{75}{3{{v}_{c}}}=\dfrac{12.5}{60} \\
 & \Rightarrow {{v}_{c}}=\dfrac{75\times 60}{3\times 12.5}=120km/hr \\
\end{align}$
Thus, the velocity of the car is 120kmph which matches option (c). Hence (c) is the correct option.

Note: We should be careful to convert the time lost by the train into hours before solving the question as all the terms in a valid equation should be in the same units.