Question : Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur, respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur, respectively. If X is moving at 45 km/hr, the speed of Y is:
Option 1: 60 km/hr
Option 2: 58 km/hr
Option 3: 54 km/hr
Option 4: 64.8 km/hr
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Correct Answer: 54 km/hr
Solution :
We know,
$\frac{\text{Speed of X}}{\text{Speed of Y}}=\sqrt{\frac{\text{Time taken by Y after crossing X}}{\text{Time taken by X after crossing Y}}}$
$⇒\frac{45}{\text{Speed of Y}}=\sqrt{\frac{\text{3 hour 20 min}}{\text{4 hour 48 min}}}=\sqrt{\frac{\text{200 min}}{\text{288 min}}}=\sqrt{\frac{100}{144}}$
$⇒\frac{45}{\text{Speed of Y}}=\frac{10}{12}$
$\therefore \text{Speed of Y}=54$ km/hr
Hence, the correct answer is 54 km/hr.
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