Question : A train covers the distance between station A and station B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then the same distance is covered in 48 minutes. The distance between stations A and B is:
Option 1: 60 km
Option 2: 64 km
Option 3: 80 km
Option 4: 55 km
Correct Answer: 60 km
Solution :
Let the distance between the two stations be $x$ km.
So, the speed of the train is $\frac{x}{\frac{45}{60}}=\frac{4x}{3}$ km/hr
According to the question,
$\frac{x}{\frac{4x}{3}-5}=\frac{48}{60}$
⇒ $\frac{x}{\frac{4x-15}{3}}=\frac{48}{60}$
⇒ $\frac{3x}{4x-15}=\frac{4}{5}$
⇒ $16x-60=15x$
⇒ $x=60$ km
Hence, the correct answer is 60 km.
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