Question
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
Answer: Option C
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Answer : Option C
Explanation :
$MF#%\begin{align}
&\text{Let speed of the car = x kmph}\\\\
&\text{Then speed of the train = }\dfrac{(100+50)}{100}x = \dfrac{150}{100}x = \dfrac{3}{2}x \text{ kmph}\\\\
&\text{Time taken by the car to travel from A to B} = \dfrac{75}{x} \text{ hours}\\\\
&\text{Time taken by the train to travel from A to B} = \dfrac{75}{\left(\dfrac{3}{2}x \right)} + \dfrac{12.5}{60}\text{ hours}\\\\
&\text{Since Both start from A at the same time and reach point B at the same time}\\\\
&\dfrac{75}{x} = \dfrac{75}{\left(\dfrac{3}{2}x \right)}+\dfrac{12.5}{60}\\\\
&\dfrac{25}{x} = \dfrac{12.5}{60}\\\\
&x = \dfrac{25 \times 60}{12.5} = 2 \times 60 = 120
\end{align} $MF#%
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