Question : A train can travel 25% faster than a car. Both start from point A at the same time and reach point B, 165 km away, at the same time. On the way, the train takes 40 minutes to stop at the stations. What is the difference in the speeds (in km/hr) of the train and car?
Option 1: 6.375 km/hr
Option 2: 7.635 km/hr
Option 3: 9.75 km/hr
Option 4: 12.375 km/hr
Correct Answer: 12.375 km/hr
Solution :
Let the speed of car = $x$ km/hr
Speed of the train = $x$ + 25% of $x$ = $\frac{5x}{4}$ km/hr
Distance = 165 km
According to the question, (since the train took 40 minutes less than the car)
$\frac{\text{Distance}}{\text{Speed of the car}}$–$\frac{\text{Distance}}{\text{Speed of the train}}$ = $\frac{40}{60}$
⇒ $\frac{165}{x}$–$\frac{165}{\frac{5x}{4}}$ = $\frac{40}{60}$
⇒ $\frac{165}{x}$–$\frac{660}{5x}$ = $\frac{2}{3}$
⇒ $\frac{825-660}{5x}$ = $\frac{2}{3}$
⇒ $\frac{165}{5x}$ = $\frac{2}{3}$
⇒ $x = \frac{99}{2}$
∴ Speed of car is $\frac{99}{2}$ km/hr
∴ Speed of train = $\frac{5}{4}×\frac{99}{2}$ = $\frac{495}{8}$ km/hr
Difference in the speed
= $\frac{495}{8}$–$\frac{99}{2}$
= $\frac{495-396}{8}$
= $\frac{99}{8}$
= $12.375$ km/hr
Hence, the correct answer is 12.375 km/hr.
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