Question : Two trains, A and B, start from stations X and Y and travel towards Y and X, respectively. After passing each other, they take 4 hours 48 minutes, and 3 hours 20 minutes respectively to reach Y and X. If train A is moving at 45 km/hr, then the speed of train B is:
Option 1: 60 km/hr
Option 2: 64.8 km/hr
Option 3: 54 km/hr
Option 4: 37.5 km/hr
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Correct Answer: 54 km/hr
Solution :
Given: Two trains, A and B, start from stations X and Y and travel towards Y and X, respectively. After passing each other, they take 4 hours 48 minutes, and 3 hours 20 minutes, respectively, to reach Y and X and train A is moving at 45 km/hr.
Let the speed of train B be $x$ km/hr.
The speed of train A is 45 km/hr.
Time taken by train A = 4 hours 48 minutes = $\frac{24}{5}$ hours.
Time taken by train B = 3 hours 20 minutes = $\frac{10}{3}$ hours.
According to the question,
$\frac{45}{x}=\sqrt{\frac{\frac{10}{3}}{\frac{24}{5}}}$
⇒ $\frac{45}{x}=\sqrt{\frac{25}{36}}$
⇒ $\frac{45}{x}=\frac{5}{6}$
⇒ $x=\frac{45×6}{5}=54$
So, the speed of train B is 54 km/hr.
Hence, the correct answer is 54 km/hr.
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